Irison,  fflafceman,  Taylor  &  Co.  '$  Publications. 


THE  AMERICAN  EDUCATIONAL   SERIES 


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admirable 
comprises 
advanced 


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FIRST  LES 
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RUDIMENT 
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ARITH  MET 
NEW  ELER 
UNIVERSIT 
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GIFT  OF 


lished  for 


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READER. 


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I  Series 


«D  CONIC 
EAL   CAL- 

RONOMY. 
TRY. 

are  pub- 


New  editions  of  the  Primary,  Common  School,  High  School,  Academic  and  Counting 

House  Dictionaries  have  recently  been  issued,  all  of  which  are 

numerously  illustrated. 


Webster's  PRIMARY  SCHOOL  DICTIONARY, 
Webster's  COMMON  SCHOOL  DICTIONARY. 
Webster's  HIGH  SCHOOL  DICTIONARY. 
Webster's  ACADEMIC  DICTIONARY. 
Webster's  COUNTING-HOUSE   AND  FAMILY 
DICTIONARY. 


Also: 

V/ebsteSs  POCKET  DICTIONARY, —  A  pic- 
torial abridgment  of  the  quarto. 

Webster's  ARMY  AND  NAVY  DICTIONARY. 
—By  Captain  E.  C.  BOYNTON,  of  West 
Point  Military  Academy. 


Zvison,  IBlafceman,  Taylor  &  Co.  's  ^Publications. 


KERL'S    STANDARD    ENGLISH   GRAMMARS. 

For  more  of  originality,  practicality,  and   completeness,  KERL'S  GRAMMARS  are 
recommended  over  others. 

GRAMMAR.  —  Designed    for    Schools 
where  only  one  text-book  is  used. 
We  also  publisJi  : 

SILL'S  NEW  SYNTHESIS;   cr,  Elementary 
Grammar. 

SILL'S  BLANK  PARSING  BOOK.— To  accom- 
pany above. 

WELLS'  (W.  H.)  SCHOOL  GRAMMAR. 

WELLS'  ELEMENTARY  GRAMMAR. 


KERL'S  FIRST  LESSONS  IN  GRAMMAR. 

KERL'S  COMMON  SCHOOL  GRAMMAR. 

KERL'S  COMPREHENSIVE  GRAMMAR. 
Rece  ntly  issued  : 

KERL'S  COMPOSITION  AND  RHETORIC. — A 
simple,  concise,  progressive,  thor- 
ough, and  practical  work  on  a  new 
plan. 

KERL'S    SHORTER    COURSE    IN    ENGLISH 


GRAY'S    BOTANICAL    TEXT-BOOKS. 

These  standard  text-books  are  recognized  throughout  this  country  and  Europe 
as  the  most  complete  and  accurate  of  any  similar  works  published.  They  are  more 
extensively  used  than  all  others  combined. 

Gray' s  u  How  PLANTS  GROW." 

Gray's  LESSONS  IN  BOTANY.  302  Draw- 
ings. 

Gray's  SCHOOL  AND  FIELD  BOOK  OF 
BOTANY. 

Gray's  MANUAL  OF  BOTANY.  20  Plates. 

Gray's  LESSONS  AND  MANUAL. 


Gray's  MANUAL  WITH  MOSSES,  &c.    Illus- 
trated. 
Gray's     FIELD,     FOREST    AND    GARDEN 

BOTANY. 
Gray's     STRUCTURAL     AND     SYSTEMATIC 

BOTANY. 

FLORA  OF  THE  SOUTHERN  STATES. 
Gray's  BOTANIST'S  MICROSCOPE.      2  Lenses. 
3 


WILLSON'S    HISTORIES. 

Famous  as  being  the  most  perfectly  graded  of  any  before  the  public. 

HISTORY.     Uni- 


;  PRIMARY  AMERICAN  HISTORY. 
;  HISTORY  OF  THE  UNITED  STATES. 
;  AMERICAN  HISTORY.     School  Edition. 
! OUTLINES  OF  GENERAL  HISTORY.    School 
Edition. 


OUTLINES    OF  GENERAL 

versity  Edition. 
WILLSON'S    CHART    OF    AMERICAN 

TORY. 
PARLEY'S  UNIVERSAL  HISTORY. 


His- 


WELLS'    SCIENTIFIC    SERIES. 

Containing  the  latest  researches  in  Physical  science,  and  their  practical  appli 
ication  to  every-day  life,  and  is  still  the  best. 


SCIENCE  OF  COMMON.  THINGS. 
NATURAL  PHILOSOPHY. 
PRINCIPLES  OF  CHEMISTRY. 
FIRST  PRINCIPLES  OF  GEOLOGY. 


Also: 

Hitchcock's  ANATOMY  AND  PHYSIOLOGY. 
Hitchcock's  ELEMENTARY  GEOLOGY. 
Eliot  &  Storer's  CHEMISTRY, 


FASQUELLE'S  FRENCH  COURSE 

Has  had  a  success  unrivaled  in  this  country,  having  passed  through  more  than 
Ifty  editions,  and  is  still  the  best. 


^asquelle's  Introductory  French  Course. 
~'~asque lie's  Larger  French  Course.     Re- 
vised. 

~<asque lie's  Key  to  the  Above, 
':rasquelle's  Colloquial  French  Reader. 
7asqueUes  Telemaque. 


Fasquelle's  Dumas'  Napoleon. 
Fasque lie's  Racine. 

Fasquelle's  Manual  of  French  Convers- 
ation. 

Howard's  Aid  to  French    Composition. 
Talbot's  French  Pronunciation. 


NEW    MANUAL 


OF  T-IE        //j     \ 


ELEMENTS  OF  ASTRONOMY, 


DESCRIPTIVE   AND  MATHEMATICAL: 


COMPRISING 


THE  LATEST  DISCOVERIES  AND  THEORETIC  VIEWS, 


WITH    DIKKCTIONS   FOR   THK 


USE  OF  THE  GLOBES,  AND  FOE  STUDYING  THE  CONSTELLATIONS. 


BY 

HENRY   KIDDLE,   A.M., 

ASSISTANT      SUPERINTENDENT      OF      SCHOOLS,     NEW      YORK 


NEW  YORK: 
IVISON,  BLAKEMAN,   TAYLOR,  &  COMPANY, 

138  &  140  GRAND  STREET. 
CHICAGO:  133  &  135  STATE  STREET. 

1871. 


Entered,  according  to  Act  of  Congress,  in  the  year  18CT,  by 

HENRY    KIDDLE 

In  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for  the  Southern 
District  of  New  York. 


Electrotyped  by  SMITH  &  McDouGAL,  82  and  84  Beekman  St.,  N.  Y. 


PREFACE. 


THIS  work  is  designed  to  take  the  place  of  the  "Manual 
of  Astronomy,"  published  by  the  author  in  1852.  In  method 
of  treatment  it  is  entirely  new,  and  is  much  more  compre- 
hensive than  the  previous  work,  containing  a  fuller  expo- 
sition of  elementary  principles,  and  embodying  the  chief 
results  of  astronomical  research  during  the  last  fifteen 
years,— a  period  exceedingly  fruitful  in  discovery. 

The  plan  is  as  far  as  possible  objective,  in  a  proper  sense  ; 
that  is,  it  is  based  upon  the  conceptions  of  the  pupil  ac- 
quired by  an  actual  observation  of  the  phenomena  of  the 
heavens,  to  which  his  attention  is  constantly  directed  ;  the 
relation  between  these  phenomena  and  the  facts  inferred 
from  them  being  clearly  shown  at  every  step.  Great  pains 
have  been  taken  to  divest  that  part  of  the  subject  which 
treats  of  the  Sphere  of  its  usual  arbitrary  and  complex 
character  by  developing  the  requisite  ideas  before  present- 
ing formal  definitions. 

Simplified  methods  of  computing  the  numerical  elements, 
such  as  periods,  distances,  and  magnitudes,  are  given 
throughout  the  work ;  in  most  cases  the  calculations  being 
made  for  the  pupil,  but  without  recourse  to  any  other  than 
elementary  arithmetic  and  the  most  rudimental  principles 
of  geometry.  These  calculations  are  based  on  the  recent 


870725 


IV  PREFACE. 

determination  of  the  solar  parallax,  and  other  elements  as 
established  by  the  latest  observations  and  researches  of  dis- 
tinguished astronomers  ;  and  it  is  believed  that,  presented 
in  this  way,  they  will  prove  valuable  as  arithmetical  exer- 
cises, as  well  as  an  important  aid  in  imparting  clear,  correct, 
and  permanent  conceptions  of  the  astronomical  truths. 

Brief  historical  sketches  of  the  various  discoveries — a 
most  fascinating  part  of  the  subject — are  given  in  connection 
with  the  facts  to  which  they  relate.  These,  with  all  other 
matter  designed  to  elucidate  or  exemplify  the  text,  are 
printed  in  smaller  type,  and  in  distinct  paragraphs,  which 
have  been  distinguished  by  letters,  so  as  to  be  readily  refer- 
red to,  and  conveniently  indicated  by  the  teacher  in  assigning 
lessons. 

The  Problems  for  the  Globes  have  been  placed  in  connection 
with  that  part  of  the  text  to  which  they  refer  and  in  which 
they  are  designed  to  exercise  the  pupil. 

The  illustrations  are  copious,  and  have  been  engraved 
specially  for  this  work,  many  from  original  drawings  and 
diagrams  ;  the  telescopic  views,  from  drawings  and  photo- 
graphs made  by  distinguished  observers.  All  the  important 
English  astronomical  works  of  recent  date  have  been 
carefully  consulted. 

The  author  hopes  that  this  little  volume,  containing  as  it 
does  a  full  exposition  of  the  recent  progress  and  present 
condition  of  the  sublimest  of  all  sciences,  will  prove  a 
useful  and  acceptable  addition  to  the  educational  facilities 
so  copiously  supplied  at  the  present  time. 

NBW  YOBK,  January  1ft,  1868. 


CONTENTS. 


INTRODUCTION. 

PAGB 

MATHEMATICAL  DEFINITIONS 9 

CHAPTER  I. 

THE  HEAVENLY  BODIES — GENERAL  PHENOMENA. 

Apparent  Motions  —  Copernican    and    Ptolemaic    Systems— Classification  of  the 
Heavenly  Bodies IT 

CHAPTER  II. 

THE  PLANETS. 
Their  Number— Classification-Direction  of  their  Motion 22 

CHAPTER  III. 

MAGNITUDES  OF  THE  SUN  AND  PLANETS. 

Their  comparative  Volume,  Mass,  and  Density.    Terrestrial  and  Major  Planets 
compared 24 


CHAPTER  IV. 

ORBITAL  REVOLUTIONS   OF  THE  PLANETS. 

Centripetal  and  Centrifugal  Forces — Kepler's  Laws — Comparative  Eccentricities  of 
the  Planetary  Orbits— Their  Inclinations — Mean  and  True  Place— Nodes 

CHAPTER  V. 

DISTANCES,  PERIODIC  TIMES,  AND  ROTATIONS  OF  THE 
PLANETS. 

Bode' s  Law— Hourly  Orbital  Velocities— Inclination  of  the  Planetary  Axes— Times 
of  Rotation— Sun's  Rotation 


yi  CONTENTS. 

CHAPTER  VI. 

ASPECTS  OF  THE  PLANETS. 

Angular  Distance— Synodic  and  Sidereal  Periods— Morning  and  Evening  Star- 
Questions  for  Exercise 43 

CHAPTER  VII. 

THE   EARTH. 

Proofs  of  its  sphericity 49 

SECTION  I. — Latitude  and  Longitude — Difference  of  Time — Problems  for  the  Globe.      k4 
SECTION  II. — The  HOBIZON — Positions  of  the  Sphere — PABALLAX — REFBACTION.  ...     54 
SECTION  III. — APPABENT  MOTIONS  OF  THE  SUN  AND  PLANETS — Daily  Phenomena — 
Apparent  Annual  Motion— Obliquity  of  the  Ecliptic— Signs  of  the   Ecliptic- 
Zodiac—  PBEOEBSION— Problems  for  the  Globe 63 

SECTION  IV.— DAY  and  NIGHT— Longest  and  Shortest  Days  and  Nights— Constant 

Day  and  Night— Twilight— Problems  for  the  Globe 73 

SECTION  V.— THE  SEASONS— Motion  of  the  Line  of  Apsides— Zones 82 

SECTION  VI.— FIGUBE  AND  SIZK  OF  THE  EABTH— Proofs  of  its  Oblatenebs— Cause 

of  Precession 88 

SECTION  VII.— TIME— Solar  and  Sidereal  Day— Equation  of  Time— Sidereal  and 
Tropical  Year— Anomalistic  Year— Questions  for  Exercise 92 

CHAPTER  VIII. 

THE   SUN. 

Its  Distance— Magnitude — Rotation— Spots — Theories  as  to  its  Physical  Constitu- 
tion—Light and  Heat— Motion  of  the  Sun  and  System  in  Space— Zodiacal  Light  99 

CHAPTER  IX. 

THE   MOON. 

Its  Distance— Eccentricity— Magnitude— Phases— Sidereal  and  Synodical  Month- 
Harvest  Moon— Rotation— Orbit— Libration— Position  of  the  Axis— Lunar  Day 
and  Night— Atmosphere— Selenography— Lunar  Mountains— Lunar  Irregu- 
larities   112 

CHAPTER  X. 

ECLIPSES. 

Cause  of  Eclipses— Solar  and  Lunar  Ecliptic  Limits— How  to  calculate  them-?- 
Number  of  Eclipses— Length  of  Shadows  of  the  Earth  and  Moon— Breadth  of 
the  same— Total  and  Partial  Eclipses— Cycle  of  Eclipses— Phenomena  pre- 
sented by  Total  Eclipses— Occultationu 131 


CONTENTS.  yii 

CHAPTER  XL 

TIDES. 

PAGE 

Attraction  of  the  Sun  and  Moon— Relative  amount  calculated— Spring  and  Neap 
Tides— Why  the  Tides  rise  later  each  day— Solar  and  Lunar  Tide- Waves— 
Primitive  and  Derivative  Tides— Velocity  of  Tide- Wave— Atmospheric  Tides.  143 

CHAPTER  XII. 

INFERIOR   PLANETS. 

MEBCUBY— Distance  calculated— Diameter,  Mass,  etc. — Rotation — Sidereal  and  Sy- 
nodic Periods  —  Light  and  Heat  —  Seasons  —  Transits.  VENUS  —  Phases- 
Distance— Magnitude— Mass— Rotation— Mountains— Atmosphere— Axis— Sea- 
sons— Transits—  Solar  Parallax— Apparent  Motions. 14£ 

CHAPTER  XIII. 

SUPERIOR   PLANETS. 

MASS— Phases— Apparent  Motions— Distance— Parallax— Period— Magnitude— Sea- 
sons—Telescopic  Appearances.  JUPITEB— Period  —  Figure— Volume,  Mass, 
etc.— Belts— Satellites— Velocity  of  Light.  SATUBN— Orbit— Period— Figure 
—Volume,  Mass,  etc.— Axis— Seasons— Belts— Rings— Satellites.  UKANUB — 
History  of  its  Discovery— Distance— Orbit— Period— Magnitude— Satellites. 
NEPTUNE— History  of  its  Discovery— Distance,  Period,  etc.— Satellite 168 

CHAPTER  XIV. 

MINOR  PLANETS. 
Their  Discovery— Distance— Orbits— Periods— Origin— Nebular  Hypothesis 199 

CHAPTER  XV. 

MUTUAL  ATTRACTIONS  OF  THE   PLANETS. 

"Problem  of  Three  Bodies"— Elements  of  a  Planet's  Orbit— Heliocentric  and 
Geocentric  Place— Variable  and  Invariable  Elements— Great  Inequality  of 
Jupiter  and  Saturn— Centre  of  Gravity— Comparative  Masses  of  the  Sun  and 
Planets 204 


Vlll  CONTENTS. 

CHAPTER  XVI. 

COMETS. 

PAGE 

Appearance — Orbits — Elements — Elliptic  Comets  of  Long  and  Short  Periods — 
Velocity  of  Comets — Number  of  Comets — Size — Masses  and  Densities — Tails  of 
Comets— REMABKABLECOMETS— Comet  of  1680— Halley's  Comet— Encke's  Comet 
— Lexell's  Comet— Comet  of  1811— Comet  of  1843— Donati's  Comet— Recent 
Comets 209 

CHAPTER  XVII. 

METEOES   OE   SHOOTING   STAES. 

Star-Showers — Meteoric  Epochs — Nature  and  Origin  of  Meteors— Their  Number — 
Fire-Bails — Aerolites — Meteoric  Dust — November  Meteors — Meteors  and  Com- 
ets compared 223 

CHAPTER  XVIIL 

THE  STAES. 

Appearance— Parallax  and  Distance — Apparent  Magnitudes — Number — Constella- 
tions—How named— Names  of  Stars— Classification  of  the  Constellations- 
History  of  each— Table  showing  their  Relative  Positions— Star-Names— List  of 
Principal  Stars— Problems  for  the  Celestial  Globe— Star-Figures— Change  in 
the  apparent  places  of  the  Stars — Nutation — Aberration  of  Light — Galaxy  or 
Milky  Way— Galactic  Circle  and  Poles— Proper  Motion  of  the  Stars— Motion 
of  Solar  System  in  Space— Central  Sun  Hypothesis— Multiple  Stars— Double 
Stars— Colored  Stars— Binary  Stars— Dimensions  of  Stellar  Orbits— Masses  of 
the  Stars— Their  Physical  Constitution— Spectrum  Analysis— Variable  Stars- 
Temporary  Stars— Star-Clusters 229 

CHAPTER  XIX. 

NEBULA. 

History  of  their  Discovery— How  distinguished  from  Clusters — Resolvable  and 
Irresolvable  Nebulse— Herschel's  Nebular  Hypothesis— Classification  of  Nebulae 
—Elliptic  Nebulae— Annular  Nebulas— Spiral  Nebulae— Planetary  Nebulae- 
Stellar  Nebula  and  Nebulous  Stars— Irregular  Nebulae— Variable  Nebulae- 
Structure  of  the  Universe 263 


INTRODUCTION. 


MATHEMATICAL    DEFINITIONS. 

1.  ASTRONOMY  *  is  that  branch  of  science  which  treats  of 
the  heavenly  bodies ;  as  the  sun,  moon,  stars,  comets,  etc. 

Before  even  the  simple  elements  of  this  science  can  be  learned,  it  is 
necessary  that  the  rudiments  of  geometry  should  be  understood ;  hence, 
the  following  definitions  are  here  presented  as  an  introduction.  For  con- 
venience of  treatment,  more  are,  however,  inserted  in  this  section  than  the 
student  will  need,  at  first,  to  apply.  The  teacher  should,  therefore,  not 
only  see  that  they  are  learned  by  way  of  preparation  for  the  general  subject, 
but  be  careful  to  recur  to  them,  when  the  pupil  reaches  the  parts  of  the 
subject  to  which  they  specially  refer. 

2.  EXTENSION,  or  magnitude,  may  be  measured  in  three 
directions  ;  namely,  length,  breadth,  and  thickness.     These 
are  therefore  called  the  dimensions  of  extension. 

a.  Length  is  the  greatest  dimension ;  Thickness,  the  shortest ; 
Breadth,  the  other. 

3.  A  LINE  is  that  which  is  conceived  to  have  only  one 
dimension. 

a.  Lines  have  no  real  existence  independently  of  extension,  or  solidity. 
They  are  purely  abstract  or  imaginary  quantities :  the  marks  called 
lines  are  only  representatives  of  them. 

4.  A  STRAIGHT  LINE  is  a  line  that  does  not  change  its 
direction  at  any  point. 


*  Derived  from  the  Greek  words  Astron,  meaning  a  star,  and  Nomos, 
meaning  a  law. 

QUESTIONS.— 1 .  What  is  astronomy  ?  2.  How  may  extension  be  measured  ?  a.  Length, 
breadth,  and  thickness,— how  distinguished  ?  3.  What  is  a  line  ?  a.  Have  lines  any 
real  existence?  4.  What  is  a  straight  line? 


DEFINITIONS. 

&  A  OURVF  LiitE  is  one  that  changes  its  direction  at 
every  point. 

6.  A  POINT  is  that  which  is  conceived  to  have  no  dimen- 
sions, but  only  position. 

a.  A  point  is  represented  by  a  dot  ( . ). 

b.  A  straight  line  measures  the  shortest  distance  between  two  points. 

7.  A  SURFACE  is  that  which  is  conceived  to  have  two 
dimensions,  length  and  breadth. 

8.  A  PLANE  SURFACE,  OR  PLANE,  is  a  surface  with  which, 
if  a  straight  line  coincide  in  two  points,  it  will  coincide 
in  all. 

a.  That  is,  a  straight  line  cannot  lie  partly  in  a  plane,  and  partly 
out  of  it ;  and  if  applied  to  it  in  any  direction,  it  will  coincide  with  it 
throughout  its  whole  extent.  The  term  plane  does  not  imply  any 
limitation,  or  boundary,  but  signifies  indefinite  direction,  without 
change,  both  as  to  length  and  breadth. 

9.  A  plane  bounded  by  lines  is  called  a  PLANE  FIGURE. 

j*ig.  i.  10.  A  CIRCLE  is  a  plane  figure  bounded 

Tangent^  by  a  curve  line  every  point  of  which  is 

equally  distant    from    a    point   within, 

called  the  centre. 

11.  The  curve  line  that  bounds  a  cir- 
cle is  called  the  CIRCUMFERENCE. 

12.  The  DIAMETER  of   a  circle  is  a 
straight  line  drawn  through  its  centre 

from  one  point  of  the  circumference  to  another. 

13.  The  RADIUS  is  a  straight  line  drawn  from  the  centre 
to  the  circumference. 

14.  An  ARC  is  any  part  of  the  circumference. 

QUESTIONS.— 5.  What  is  a  curve  line?  6.  A  point?  n.  Hour  represented ?  b.  The 
shortest  distance  between  two  points?  7.  What  is  a  surface?  8.  A  plane  surface? 
a.  Does  the  term  plane  imply  any  limit?  9.  What  is  a  plane  figure?  10.  What  is  a 
circle?  11.  What  is  meant  by  the  circumference?  12.  The  diameter?  13.  The  radius? 
14.  What  Is  an  arc? 


MATHEMATICAL     DEFINITIONS. 


li 


Pig.  2. 


15.  A  TANGENT  is  a  line  which  touches  the  circumference 
in  one  point. 

16.  A  SEMICIRCLE  is  one-half  of  a  circle ;  a  QUADRANT  is 
a  quarter  of  a  circle. 

17.  The  circumference  of  a  circle  is  supposed  to  be  divided 
into  360  degrees,  each  degree  into  60  minutes,  and  each 
minute  into  60  seconds. 

a.  Degrees  are  marked  (  °  ) ;  minutes,  ( ' )  ;  and  seconds,  (  "  ). 

18.  An  ANGLE  is  the  difference  in  direc- 
tion of  two  straight  lines  that  meet  at  a 
point,  called  the  vertex. 

a.  It  is  of  the  greatest  importance  that  the  student 
of  Astronomy  should  form  a  clear  idea  of  an  angle, 
since  nearly  the  whole  of  astronomical  investigation  is  based  upon  it 
The  apparent  distance  of  two  objects  from  each  other,  as  seen  from  a 
remote  point  of  view,  depends  upon  the  difference  of  direction  in  which 
they  are  respectively  viewed  ;  that  is  to  say,  the  angle  formed  by  the 
two  lines  conceived  to  be  drawn  from  the  objects,  and  meeting  at  the 
eye  of  the  observer.  This  is  called  the  angular  distance  of  the  objects, 
and,  as  will  readily  be  understood,  increases  as  the  two  objects  depart 
from  each  other  and  from  the  general  line  of  view. 

Pig.  3. 


19.  The  ANGLE  OF  VISION,  or  VISUAL  ANGLE,  is  the 

QUESTIONS.- 15.  What  is  a  tangent?  16.  A  semicircle?  A  quadrant?  IT.  How 
Is  the  circumference  conceived  to  be  divided?  «.  How  are  degrees,  minutes,  and 
seconds  marked?  18.  What  is  an  angle?  «.  Its  importance  in  astronomy?  What  is 
angular  distance  ?  19.  What  is  the  angle  of  vision  ? 


MATHEMATICAL     DEFINITIONS. 


angle  formed  by  lines  drawn  from  two  opposite  points  of  a 
distant  object,  and  meeting  at  the  eye  of  the  observer. 

ft.  It  will  be  easily  seen  that,  as  the  apparent  size  of  a  distant  object 
depends  upon  the  angle  of  vision  under  which  it  is  viewed,  it  must 
dimmish  as  the  distance  increases,  and  vice  versa. 

Thus,  the  object  A  B  (Fig.  3)  is  viewed  under  the  angle  A  P  B,  which 
determines  its  apparent  size  in  that  position  ;  but  when  removed  farther 
from  the  eye,  as  at  C  D,  the  angle  of  vision  becomes  C  P  D,  an  angle  ob- 
viously smaller  than  A  P  B,  and  hence  the  object  appears  smaller.  At  E  F, 
the  object  appears  larger,  because  the  visual  angle  E  P  F  is  larger.  The 
farther  the  object  is  removed,  the  less  the  divergence  of  the  lines  which 
form  the  sides  of  the  angle  ;  and  the  nearer  the  object  is  brought  to  the  eye, 
the  greater  the  divergence  of  the  lines. 

20.  An  angle  is  measured  by  drawing  a  circle,  with  the 
vertex  as  a  centre,  and  with  any  radius,  and  finding  the 
number  of  degrees  or  parts  of  a  degree,  included  between 
the  sides. 

21.  A  RIGHT  ANGLE  is  one  that  con- 
tains 90  degrees,  or  one-quarter  of  the 
circumference. 

22.  When  one  straight  line  meets  an- 
other so  as  to  form  a  right  angle  with  it, 
it  is  said  to  be  PERPENDICULAR. 

23.  A  straight  line  is  said  to  be  per- 
pendicular to  a  circle  when  it  passes,  or 
would  pass  if  prolonged,  through    the 
centre. 

24.  An  angle  less  than  a  right  angle  is 
called  an  ACUTE  ANGLE;    one  greater 
than  a  right  angle  is  called  an  OBTUSE 
.ANGLE. 

QUESTIONS.— a.  How  dependent  on  the  distance  of  an  object?  Explain  from  the  dia- 
gram. 20.  How  is  an  angle  measured  ?  2L  What  is  a  right  angle  ?  22.  When  is  one 
line  perpendicular  to  another  ?  23.  When  is  a  straight  line  perpendicular  to  a  circle  ? 
24.  What  is  au  acute  angle  ?  An  obtuse  angle  ?  Illustrate  by  Fig.  T. 


Fig.  4. 


Fig.  5. 


Fig.  6. 


MATHEMATICAL     DEFINITIONS. 


13 


Pig.  7- 


In  the  annexed  diagram,  the  semi-cir- 
cumference is  used  to  measure  all  the 
angles  having  their  vertices,  or  angular 
points,  at  C.  Thus  BCD,  containing 
the  arc  B  D,  is  an  angle  of  45° ;  B  C  E, 
an  angle  of  90° ;  and  B  C  F,  of  130°. 
The  points  A  and  B  are  at  the  angular 
distance  of  180°,  or  two  right  angles 
from  each  other. 


25.  A   TRIANGLE    is 
bounded  by  three  sides. 


a    plane    figure 


Fig.  8. 


Angled 
Triangle 


Fig.  9. 


Fig.  10. 


Parallel  Lines . 


Fig.  11. 


a.  The  sum  of  the  three  angles  of  every  trian- 
gle is  equal  to  two  right  angles. 

6.  A  triangle  that  contains  a  right  angle  is 
called  a  Right-angled  Triangle. 

C.  A  triangle  having  equal  sides  is  called  an 
Equilateral  Triangle. 

d.  Each  of  the  angles  of  an  equilateral  triangle 
is  an  angle  of  60°  ;  since  the  three  angles  are 
equal  to  each  other,  and  their  sum  is  equal  to 
180°. 

26.  PARALLEL  LINES   are   those  situ- 
ated in  the  same  plane,  and  at  the  same 
distance  from  each  other,  at  all  points. 

a.  Parallel  lines  may  be  either  straight   or 
curved. 

b.  The    circumferences  of  concentric  circles, 
that  is,  circles  drawn  around  the  same  centre,  are 
parallel. 

27.  AN  ELLIPSE  is 'a  curve  line,  from  any  point  of  which 
if  straight  lines  be  drawn  to  two  points  within,  called  the 
foci,  the  sum  of  these  lines  will  be  always  the  same. 

QUESTIONS.— 25.  What  is  a  triangle  ?  a.  Sum  of  its  three  angles  ?  b.  What  is  a  right- 
angled  triangle  ?  c.  An  equilateral  triangle  ?  d.  The  value  of  each  of  its  angles  ?  Why  ? 
26.  What  are  parallel  lines?  a.  Are  they  always  straight?  6.  When  are  circles  par- 
allel ?  27.  What  is  an  ellipse  ? 


14 


MATHEMATICAL     DEFINITIONS. 


The  curve  line  D  B  E  G  represent? 
an  ellipse,  the  sum  of  the  two  straight 
lines  drawn  to  F  and  F,  the  foci,  from 
the  points  A,  B,  and  C,  respectively, 
being  always  equal.  This  sum  is  equal 
to  the  longest  diameter,  D  E. 

28.  The  longest  diameter  of 
an  ellipse  is  called  the  MAJOR  * 
Axis ;  f  and  the  shortest  diam- 
eter, the  MINOR*  Axis. 

In  the  diagram,  D  E  is  the  major  axis,  and  B  G  the  minor  axis. 

29.  The  distance  from  either  of  the  foci  to  the  centre  of 
the  ellipse  is  called  the  ECCENTRICITY  J  of  the  ellipse. 

a.  It  will  be  readily  seen  that  the  greater  the  eccentricity  of  an 
ellipse,  the  more  elongated  it  is,  and  the  more  it  differs  from  a  circle  ; 
while,  if  the  eccentricity  is  nothing,  the  two  foci  come  together,  and 
the  ellipse  becomes  a  circle. 

b.  The  distance  from  the  extremity  of  the  minor  axis  to  either  of  the 
foci  is  always  equal  to  one-half  of  the  major  axis. 

In  the  above  diagram,  F  O  is  the  eccentricity,  and  B  F  is  equal  to  D  O. 
The  amount  of  eccentricity  of  any  ellipse  is  ascertained  by  comparing  it 
with  one-half  the  major  axis.  Thus,  in  the  diagram,  O  F  being  about  one 
half  of  O  D,  the  eccentricity  of  the  ellipse  may  be  nearly  expressed  by  .5. 

30.  A  SPHERE,  or  GLOBE,  is  a  round  body  every  point  of 
the  surface  of  which,  is  equally  distant  from  a  point  within, 
called  the  centre. 

31.  A  HEMISPHERE  is  a  half  of  a  globe. 

32.  The  DIAMETER  of  a  sphere  is  a  straight  line  drawn 


*  Major  and  Minor  are  Latin  words,  meaning  greater  and  less. 
t  A  Latin  word  meaning  an  axle,  that  on  which  any  thing  turns. 
J  From  the  Greek,  ec,  from,  and  centron,  the  centre. 

QUESTIONS.— 28.  What  is  the  major  axis?  The  minor  axis?  29.  What  is  meant  by 
eccentricity  ?  a.  What  does  it  show  ?  ft.  Distance  of  foci  from  the  extremity  of  minor 
axis?  Explain  from  the  diagram.  30.  What  is  a  sphere  ?  31 .  A  hemisphere  ?  32.  The 
diameter  of  a  sphere  ? 


MATHEMATICAL     DEFINITIONS. 


15 


through  the  centre,  and  ter- 
minated both  ways  by  the  sur- 
face of  the  sphere. 

33.  The  RADIUS  of  a  sphere  is 
a  straight  line  drawn  from  the 
centre  to  any  point  of  the  surface. 

34.  Circles  drawn  on  the  sur- 
face of  a  sphere  are  either  GREAT 
CIRCLES  or  SMALL  CIRCLES. 

35.  GREAT  CIRCLES  are  these 
whose  planes  divide  the  sphere 
into  equal  parts. 

36.  SMALL  CIRCLES  are  those  whose 
sphere  into  unequal  parts. 

37.  The  POLES  OF  A  CIRCLE 
are  two  opposite  points  on  the 
surface  of  the  sphere,  equally  dis- 
tant from  the  circumference  of 
the  circle. 

«.  The  poles  of  a  great  circle  are,  of 
course,  90°  distant  from  every  point 
of  its  circumference. 

b.  Two  circles  of  the  sphere  are  par- 
allel when  they  are  equally  distant  from  each 
other  at  every  point. 

c.  Two  circles  are  perpendicular  to  each  other 
when  their  planes  are  perpendicular,  or  at  right 
angles  with  each  other. 

d.  The  Plane  of  a  Circle  or  any  other  figure 
is  the  indefinite  plane  surface  on  which  it  may 
be  conceived  to  be  drawn. 


planes  divide  the 

Fig.  14. 


PEBPENDICTJLAB  PLANKS. 


Pig-    15. 


PLANES  OF  OBEAT  CIECLE8. 


QUESTIONS. — 33.  What  is  the  radius  f  34.  How  are  circles  of  the  sphere  divided  ? 
85.  What  are  great  circles  ?  36.  Small  circles  ?  37.  Poles  of  a  circle  ?  a.  Poles  of  a 
great  circle  ?  b.  When  are  circles  of  the  sphere  parallel  ?  e.  When  perpendicular  ? 
d.  What  is  meant  by  the  plane  of  a  circle? 


16 


MATHEMATICAL     DEFINITIONS. 


38.  A  SPHEROID  *  is  a  body  resembling  a  sphere. 
Pig.  16.  39-  There  are  two  kinds  of  spheroids ; 

OBLATE  and  PROLATE  Spheroids. 

40.  An  OBLATE  SPHEROID  is  a  sphere 
flattened  at  two  opposite  points,  called  the 
poles. 

41.  A  PROLATE  SPHEROID  is  a  sphere 
extended  at  two  opposite  points. 

Thus,  an  orange  is  a  kind  of  oblate  spheroid ;  and  an  egg,  a  kind  of 
prolate  spheroid. 


*  Spheroid  means  like  a  sphere.     Old  is  from  the  Greek  word  eido,  mean- 
ing to  resemble. 


QUESTIONS. — 38.  What  is  a  spheroid  ?    39.  How  many  kinds  of  spheroids  ?    40.  What 
it  an  oblate  spheroid  ?    41.  A  prolate  spheroid  ? 


CHAPTER  I. 

THE  HEAVENLY  BODIES — GENERAL  PHENOMENA. 

1.  The  SUN,  the  MOON,  and  the  STARS,  are  the  most 
conspicuous  bodies  of  which  astronomy  treats. 

a.  Antiquity  of  the  Science. — The  various  appearances  presented 
by  these  bodies  must  always  have  engaged  the  attention  of  mankind. 
The  sublime  spectacle  of  the  starry  heavens  would  naturally,  in  the 
earliest  times,  excite  the  admiration  of  the  most  careless  or  ignorant 
observer ;  and  the  curiosity  of  mankind  would  be  early  aroused  to 
ascertain  the  nature  of  those  "  refulgent  lamps  "  which  lend  so  much 
splendor  and  beauty  to  the  otherwise  sombre  gloom  of  night. 

Hence,  we  find  that  astronomy  is  a  very  ancient  science.  The  shep- 
herds of  Chaldea,*  and  the  priests  of  Egypt  and  India,  had,  in  remote 
antiquity,  made  some  progress  in  astronomical  discovery ;  and,  it  is 
said,  Chinese  observations  are  on  record  that  date  back  more  than 
1000  years  before  Christ. 

b.  Ordinary  Phenomena. — The  most    obvious  phenomena  f  con- 
nected with  these  bodies  are  their    rising  and  setting,  and  their 
constant  motion  in  the  same  general  direction  from  one  side  of  the 
heavens  to  the  other  ;  and  consequently  these  appearances  were  prob- 
ably among  the  first  that  incited  to  scientific  inquiry. 

c.  The  Earth's  Rotation.— The  simple  fact   that  the  earth— the 
body  on  which  we  are  placed — turns  round  once  every  twenty-four 
hours,  clears  away  all  difficulty  in  explaining  these  daily  appearances ; 
but  it  was  not  until  comparatively  recent  times  that  mankind  could  be 
brought  generally  to  accept  this  truth. 

As  late  as  1633,  it  was  deemed  irreligious  to  believe  in  the  motions 


*  A  country  of  antiquity,  situated  between  the  Euphrates  and  Tigris 
rivers. 
t  Phenomena,  plural  of  phenomenon,  a  Greek  word  meaning  an  appearance. 

QUESTIONS.— 2.  Which  are  the  most  conspicuous  of  the  heavenly  bodies  ?  a.  Astron- 
omy— why  an  ancient  science  ?  b.  What  are  the  most  obvious  phenomena  ?  e.  The 
earth's  rotation— what  does  it  explain  ?  Galileo  ? 


18  THE    HEAVENLY     BODIES. 

of  the  earth. ;  and  Galileo,  in  his  seventieth  year,  was  imprisoned,  and 
finally  compelled  to  acknowledge  himself  as  guilty  of  error  and  heresy 
in  teaching  this  astronomical  truth. 

d.  The  Stars  appear  to  keep  very  nearly  the  same  situations  with 
respect  to  each  other ;  and  hence  were  called  Fixed  Stars,  to  distin- 
guish them  from  other  bodies  which  resemble,  in  their  general  appear- 
ance, stars,  but  seem  to  move  about  in  the  heavens,  at  one  time  being 
near  one  star,  then  another,  now  moving  in  one  direction,  then  in 
another ;  thus,  as  it  were,  wandering  about  in  the  heavens.  For  this 
reason,  such  bodies  were  called  planets,  or  wandering  stars. 

[In  the  Greek  language,  planetes  means  a  wanderer.  The  term  fixed  stars 
is  now  but  little  used  by  astronomers  ;  and  in  this  work,  when  the  term 
stars  is  used,  it  is  intended  to  designate  fixed  stars.] 

2.  The  apparent  motions  of  the  sun,  planets,  and  stars 
are  explained  by  supposing,  1.  That  the  earth  is  a  sphere,  or 
nearly  so  ;  2.    That  it  turns  on  its  axis ;    3.  That  the  earth 
and  planets  revolve  around  the  sun ;  and,  4.  That  the  stars 
are  situated  at   an   immense   distance   from   the  sun  and 
planets,  in  the  regions  of  space, — a  distance  so  vast  that  their 
movements  with  respect  to  each  other  can  not  generally  be 
discerned. 

3.  The  sun  with  all  the  bodies  revolving  around  it,  is 
called  the  SOLAE*  SYSTEM. 

a.  Copernican  System. — This  arrangement  of  the  sun  in  the  centre 
with  the  planets  revolving  around  it,  is  sometimes  called  the  Coper- 
nican System,  from  Nicholas  Copernicus,  who,  in  1543,  revived  the  doc- 
trine taught  by  Pythagoras,  a  Greek  philosopher,  more  than  2,000 
years  before,  that  the  sun  is  the  central  body,  and  that  the  earth  and 
planets  revolve  around  it. 

6.  Ptolemaic  System.— Previous  to  Copernicus,  the  general  belief, 
for  more  than  two  thousand  years,  had  been  that  the  earth  is  the  cen- 


From  the  Latin  word  Sol,  meaning  the  sun. 


QUESTIONS.— d.  Stars  and  planets— how  distinguished  ?  What  does  planet  mean  ? 
2.  How  are  the  apparent  motions  of  the  sun,  planets,  and  stars  explained  ?  3.  What  is 
the  solar  system  ?  a.  The  Copernican  system — why  so  called  ?  Pythagoras  ?  b.  The 
Ptolemaic  system — why  so  called  ?  Describe  it. 


THE    HEAVENLY    BODIES. 


tre  of  the  universe,  and  that  all  the  other  bodies  revolve  around  it,  in 
the  following  order:  the  moon,  then  the  sun  and  planets  in  their 
order,  and  then  the  stars.  Each  of  these  bodies  was  conceived  by 
Aristotle  to  be  set  in  a  hollow,  crystalline  sphere,  perfectly  transparent, 
by  which  it  was  carried  around  the  earth  and  prevented  from  falling 
upon  it.  This  celebrated  system  is  very  ancient,  but  being  advocated 
and  illustrated  by  Ptolemy,  an  eminent  astronomer  who  flourished  at 
Alexandria,  in  Egypt,  about  140  A.D.,  it  was  subsequently  called  the 
Ptolemaic  System. 

c.  The  Invention  of  the  Telescope.— The  doctrine  of  Copernicus, 
as  promulgated  in  his  great  work,  styled  the  "Revolutions  of  the 
Celestial  Orbs,"  published  in  1543,  was  at  first  generally  rejected,  and 
despised  as  visionary  and  absurd ;  but  the  invention  of  the  telescope,  in 
1610,  and  the  discoveries  made  by  means  of  it,  by  Galileo  and  others, 
afforded  abundant  evidence  of  the  truth  of  this  hypothesis. 
Pig.  17. 

4.  PLANETS  are  bodies  that  re- 
volve around  the  sun. 

6.  The  path  in  which  we  may 
conceive  a  planet  to  revolve  is 
called  its  orbit. 

6.  The  planets  all  revolve  around 
the  sun  in  the  same  direction,  in 
orbits  nearly  circular,  and  situated 
in  nearly  the  same  plane. 


A  PLANET'S  ORBIT. 
Fig.  18. 


A  COMET'S  ORBIT. 


a.  Comets'  Orbits. — In  these  respects 
they  differ  from  Comets,  which  also  re- 
volve around  the  sun,  but  in  different 
directions,  in  widely  different  planes,  and 
in  very  elongated,  or  eccentric  orbits ; 
that  is,  elliptical  orbits  of  great  eccen- 
tricity. [See  Introduction,  Art.  29.] 

7.  There  are  two  kinds  of  planets ; 
Primary  and  Secondary  Planets. 


QUESTIONS. — c.  What  is  said  of  the  telescope  T  4.  What  are  planets?  5.  What  is 
the  orhit  of  a  planet  ?  6.  How  do  the  planets  revolve  ?  n.  Comets'  orbits  ?  7.  How 
many  kinds  of  planets  ? 


THE     HEAVENLY     BODIES.  21 

8.  PKIMARY  PLANETS  are  those  that  revolve  around  the 
sun  only. 

9.  SECONDARY  PLANETS,  generally  called  SATELLITES,* 
are  those  that  revolve  around  their  primaries,  and,  with 
them,  around  the  sun. 

The  moon  is  an  example  of  a  secondary  planet.  It  is  the  earth's 
satellite,  its  revolution  around  the  earth  being  clearly  indicated  by 
the  changes  which  it  undergoes  each  month. 

10.  The  Solar  System  is  thus  composed  of  the  sun,  the 
primary  planets,  the  secondary  planets,  and  the  comets; 
while  the  stars  are  bodies  situated  at  an  immense  distance 
beyond  the  system. 

11.  All  the  heavenly  bodies  may  be  divided  into  two  gen- 
eral classes;  namely,  LUMINOUS  BODIES  and  OPAQUE  BODIES. 

12.  Luminous  bodies  are  such  as  shine  by  their  own  light ; 
opaque  bodies  are  such  as  shine  by  reflecting  the  light  of 
some  luminous  body. 

a.  The  sun  is  evidently  a  luminous  body  ;  for  we  receive  from  it 
both  light  and  heat,  and  in  every  position  it  presents  a  resplendent  cir- 
cular surface,  called  its  Disc.     The  moon  is  as  evidently  opaque,  since 
it  does  not  always  exhibit  an  entire  disc,  but  various  portions  of  it  at 
different  times,  such  portions  being  called  PJiasea. 

b.  The  stars  present  no  disc,  but  only  luminous  points,  shining  with 
that  twinkling  light  which  indicates  their  intense  brilliancy  and  vast 
distance.    They  are  believed  to  be  luminous  bodies,  since  we  can  dis- 
cover no  body  from  which  they  could  receive  their  light ;  and,  more- 
over, the  light  itself  which  they  emit  has  different  properties  from 
those  possessed  by  reflected  light. 

c.  The  planets,  though  in  general  appearance  resembling  the  stars, 
may  readily  be  distinguished  from  them  by  their  steady  light.    When 
viewed  through  a  telescope,  some  of  them  exhibit  phases  like  those 
of  the  moon. 

*  From  the  Latin  word  satdles,  (plural,  satellites,}  meaning  a  guard. 


QUESTIONS. — 8.  What  are  primary  plaricts ?  9.  Secondary  planets?  10.  Of  what  is 
the  solar  system  composed ?  Where  are  the  stars  situated?  11.  What  general  divi« 
sion  of  the  heavenly  bodies  ?  12.  What  are  luminous  bodies  ?  Opaque  bodies  ?  a.  Proof 
that  the  sun  is  luminous?  That  the  moon  is  opaque?  6.  Proof  that  the  stars  are 
luminous  ?  c.  Light  of  planets— how  distinguished  from  that  of  stars  ? 


CHAPTER   II. 

THE   PLANETS. 

13.  There  are  eight  large  primary  planets  in  the  solar 
system,  besides  a  great  number  of  smaller  ones,  called  MINOR 
PLANETS,  or  ASTEROIDS.* 

14.  The  names  of  the  eight  large  primary  planets,  in  the 
order  of  their  distances  from  the  sun,  are  Mercury,  Venus, 
the  Earth,  Mars,  Jupiter,  Saturn,  Uranus,  and  Neptune. 

15.  All  the  primary  planets  except  the  earth  are  divided 
into  two  classes,  INFERIOR  and  SUPERIOR  PLANETS. 

16.  Mercury  and  Venus  are  called  inferior  planets,  because 
they  revolve  within  the  orbit  of  the  earth ;  Mars,  Jupiter, 
Saturn,  Uranus,  and  Neptune  are  called  superior  planets, 
because  they  revolve  beyond  the  orbit  of  the  earth.     Instead 
of  the  terms  inferior  and  superior,  interior  and  exterior  are 
sometimes  used. 

(t,  Vulcan. — A  planet  inferior  to  Mercury  has  been  supposed  to 
exist ;  and  in  1859,  a  French  astronomer  was  thought  by  some  to  have 
discovered  it.  Later  observations  have  not,  however,  confirmed,  but 
rather  disproved,  its  existence.  The  name  given  to  this  supposed 
planet  is  Vulcan. 

17.  The  MINOR  PLANETS  are  very  small  planets  which 
revolve  around  the  sun,  between  the  orbits  of  Mars  and 
Jupiter.     Ninety-six  have  been  discovered  (1868). 

a.  These  small  planets  were  at  first,  and  have  been,  very  generally, 
called  Asteroids  ;  they  have  also  been  called  Planetoids.  The  name 

*  From  the  Greek  aster,  meaning  a  star,  and  eido,  to  resemble. 

QUESTIONS.— 13.  How  many  primary  planets  in  the  solar  system  ?  14.  What  are  the 
names  of  the  large  planets  ?  15.  How  divided  ?  16.  Which  are.  called  inferior  ?  Which 
superior?  Why?  a.  Vulcan— what  is  said  of  it?  IT.  What  are  the  minor  planets f 
Their  number  ?  a.  What  other  names  are  applied  to  them  ? 


THE     PLANETS.  23 

above  given  has,  however,  been  extensively  used  by  astronomers,  and 
appears  to  be  the  most  significant  and  appropriate. 

18.  All  the  primary  planets  revolve  around  the  sun  in  the 
direction  which  is  design ated/row  west  to  east. 

a.  It  is  difficult  to  fix  definitely  the  direction  of  circular  motion, 
since  when  viewed  in  one  position  it  may  seem  to  be  from  left  to  right 
(as  the  hands  of  a  clock  move),  and  in  another,  from  right  to  left.     The 
motion  of  the  planets,  as  we  view  them,  is  from  right  to  left, — the  reverse 
direction  of  the  hands  of  a  clock.     This  is  the  direction  indicated  in  the 
diagrams  of  this  work. 

b.  East  is  at  or  near  where  the  sun  rises  ;  West,  at  or  near  where 
it  sets.     South  is  in  the  direction  of  the  sun's  place  at  noon  ;  North, 
directly  opposite  the  south.     If  we  stand  so  as  to  face  the  north,  the  south 
will  be  behind  us,  the  east  on  the  right  hand,  and  the  west  on  the  left. 

19.  Secondary  planets,  or  satellites,  have  two  motions: 
one  around  their  primaries,  and  another,  with  them,  around 
the  sun. 

20.  Eighteen  satellites  are  known  to  exist  in  the  Solar 
System :  the  earth  has  one,  called  the  moon ;  Jupiter  has 
four ;  Saturn,  eight ;  Uranus,  four ;  and  Neptune,  one. 

a.  While  Uranus  is  undoubtedly  attended  by  at  least  four  satellites, 
there  is  a  very  great  uncertainty  as  to  the  exact  number  which  belong 
to  it.  Sir  William  Herschel,  by  whom  this  planet  was  discovered,  in 
the  latter  part  of  the  last  century,  detected,  as  he  thought,  six  satel- 
lites ;  but  only  two  of  these  have  been  observed  by  ether  astronomers, 
which,  with  two  others  discovered  by  Lassell  in  1853,  make  the  four 
referred  to  in  the  text. 

21.  The  satellites  of  the  earth,  Jupiter,  and  Saturn  re- 
yolve  around  their  primaries  from  west  to  east;  those  of 
Uranus  and  Neptune,  from  east  to  west. 

a.  With  the  exception  of  the  satellites  of  Uranus,  and  the  satellite 
of  Neptune,  all  the  planets  of  the  Solar  System  revolve  in  the  same 
direction,  that  is,  from  west  to  east. 

QUESTIONS.— 18.  What  is  the  direction  of  the  planets'  motion?  a.  How  defined? 
b.  What  is  meant  by  Eastt  West?  South?  North t  19.  What  motions  have  satel. 
lites  ?  20.  How  many  are  known  to  exist  ?  Enumerate  them  ?  a.  Satellites  of  Uranus  ? 
21.  In  what  direction  do  the  satellites  revolve?  a.  What  uniformity  of  motion  in  the 
solar  system  ? 


CHAPTER   III. 

MAGNITUDES  OF  THE  SUN  AND  PLANETS. 

22.  The  SUN  is  by  far  the  largest  body  in  the  Solar  Sys- 
tem, being  more  than  500  times  as  large  as  all  the  planets 
taken  together. 

23.  Its  diameter  is  a  little  more  than  850,000  miles. 

p.     ie  24.  The  LAKGEST 

PLANET  is  Jupiter,  its 
diameter  being  85,000 
miles,  or  one-tenth  as 
large  as  that  of  the 
sun. 

a.  Volume,  Mass, 
Density. — The  diameter 
of  Jupiter  being  one-tenth 
as  large  as  the  sun's,  its 
volume,  or  bulk,  is  one  one- 
thousandth  (.001)  that  of 
the  sun  ;  since  it  is  only 
one-tenth  as  great  in  each 
dimension , — length, 
breadth,  and  thickness  ; 

COMPARATIVE  SIZE  OF   8TTN  AND  JTTPITEB. 

and   fo  *  -iV  x  -fa  -  y-oVo. 

This  is  expressed  generally  by  saying  that  solid  bodies  of  similar  shape 
are  in  proportion  to  the  cubes  of  their  like  dimensions. 

b.  The  volume  of  a  body  is  the  amount  of  space  which  it  occupies, 

QUESTIONS  — 22.  What  is  the  comparative  size  of  the  sun?  23.  Length  of  its  diam- 
eter ?  24.  Which  is  the  largest  planet  ?  Its  diameter  ?  a.  Comparative  volume  of  the 
sun  and  Jupiter  ?  How  found  ?  6.  Define  volume. 


SUN    AND     PLANETS.  25 

as  indicated  by  its  length,  breadth,  and  thickness.     The  volumes  of 
bodies  are  in  proportion  to  the  products  of  their  three  dimensions. 

c.  Two  bodies  may  be  equal  in  volume,  but  contain  very  different 
quantities  of  matter,  owing  to  the  different  degrees  of  compactness  of 
their  substance.    Thus,  a  piece  of  cork,  equal  in  bulk  to  a  piece  of  lead, 
contains  only  about  ^  as  much  matter.     The  quantity  of  matter  which 
a  body  contains  is  called  its  mass ;  the  degree  of  compactness  of  its 
subtance  is  called  Us  density. 

d.  The  mass  of  a  body  depends  upon  its  volume  and  density  con- 
sidered conjointly.    Thus,  if  the  volumes  of  two  bodies  are  as  2  to  3, 
and  their  densities,  as  1  to  5,  their  masses  will  be  as  1  X  2  to  3  X  5,  or 
as  2  to  15 ;  that  is  to  say,  the  mass  of  the  second  will  be  7£  times  as 
great  as  that  of  the  first. 

25.  The  following  are  the  diameters  of  the  large  primary 
planets  in  miles : — 

[These  are  given  in  round  numbers  so  as  to  be  easily  remembered ;  a  more 
exact  statement  will  be  found  in  another  part  of  this  work.  It  is  im- 
portant that  the  student  should  carefully  commit  to  memory  these  num- 
bers, since  the  relative  magnitudes  of  the  planets  form  the  basis  of  much 
of  the  reasoning  in  respect  to  the  solar  system.] 

1.  Jupiter,  .  .  85,000.  5.  Earth,    .  .  7,912. 

2.  Saturn,   .  .  70,000.  6.  Venus,   .  .  7,500. 

3.  Neptune,  .  37,000.  7.  Mars,  '   .  .  4,300. 

4.  Uranus,  .  .  33,000.  8.  Mercury,  .  3,000. 

a.  Mzy'or  and  Terrestrial  Planets.— The  first  four  of  these  planets, 
it  will  be  seen,  are  very  much  larger  than  the  remaining  four,  and  are, 
for  this  reason,  sometimes  called  the  Major  Planets  ;  while  the  others, 
ueing  in  the  vicinity  of  the  earth,  are  sometimes  called  the  Terrestrial 
Planets. 

b.  Illustration. — A  clear  idea  of  the  comparative  size  of  the  sun 
and  planets  may  be  obtained  by  conceiving  the  sun  to  be  a  globe 
two  feet  in  diameter.    Mercury  and  Mars  would  then  be  of  the  size  of 
pepper-corns ;  the  earth  and  Venus,  of  the  size  of  peas ;  Jupiter  and 


QUESTIONS.— c.  What  is  meant  by  the  mass  of  a  body  ?  Its  density  ?  d.  On  what 
does  mass  depend  ?  25.  State  the  diameter  of  each  planet  Name  the  planets  in  the 
order  of  size.  a.  Which  are  called  major  planets  ?  Terrestrial  planets  ?  b.  Give  an 
illustration  of  the  comparative  size  of  the  sun  and  planets. 


26  MAGNITUDES     OF    THE 

Saturn,  as  large  as  oranges  ;  and  Neptune  and  Uranus,  as  large  as  full 
sized  plums.     [See  figure,  page  19.] 

26.  The  MINOR  PLANETS,  or  ASTEROIDS,  are  all  of  very 
small  size,  the  diameter  of  the  largest  not  exceeding  300 
miles,  and  that  of  the  smallest  being  only  a  very  few  miles. 

(l.  Entire  Mass  of  the  Minor  Planets. — It  lias  been  computed  by 
the  celebrated  French  mathematician,  Le  Verrier,  that  their  entire 
mass,  however  many  may  exist,  can  not  exceed  one-fourth  that  of  the 
earth.  This  calculation  is  based  on  the  amount  of  disturbance  occa- 
sioned by  their  united  attraction,  in  the  motions  of  the  Earth  and 
Mars.  Now,  the  diameter  of  the  largest  being  only  about  840  of  the 
diameter  of  the  earth,  its  volume  must  be  only  ygoffiT  of  the  earth's  ; 
and  hence,  it  would  require  4,750  planets  as  large  as  the  largest  of  the 
asteroids  to  equal  the  amount  specified  by  the  mathematician. 

27.  All  the  SATELLITES  are  smaller  than  Mars,  and  with 
the  exception  of  two,  one  of  Jupiter's  and  one  of  Saturn's, 
are  smaller  than  Mercury. 

a.  The  diameter  of  the  moon  is  2,160  miles  ;  the  four  satellites  of 
Jupiter,  excepting  one,  are  larger  than  the  moon  ;  and  the  eight  satel- 
lites of  Saturn,  excepting  one,  are  smaller  than  the  moon. 

28.  The  following   presents  a  comparative  view    of  the 
densities  of  the  primary  planets,  as  compared  with  that  of 
water : 

1.  Mercury,  .     .  6J.  5,  Jupiter,    .  .  1|. 

2.  Venus,      .    .  5|.  6.  Uranus,   .  .  1. 

3.  Earth,  .     .     .  5|.  7.  Neptune,  .     7V 

4.  Mars,    ...  4.  8.  Saturn,    .  .    f. 

ft.  It  will  be  seen  that  the  terrestrial  planets  are  all  of  considerably 
greater  density  than  the  major  planets  ;  and  that  the  densities  dimin- 
ish, with  the  exception  of  Saturn,  as  the  distance  of  the  sun  increases. 


QUESTIONS. — 26.  What  is  the  size  of  the  minor  planets?    a.  Their   entire  mass? 

27.  What  is  the  comparative  size  of  the  satellites  ?    a.  What,  compared  with  the  moon  ? 

28.  What  is  the  density  of  each  of  the  primary  planets  ?    a .  Density  of  the  terrestrial 
planets  compared  with  that  of  the  major  planets  ? 


SUN     AND     PLANETS.  27 

29.  The  density  of  the  sun  is  only  one-fourth  that  of  the 
earth,  or  about  1£  that  of  water.  The  density  of  the  moon 
is  about  3^  that  of  water. 

a.  Masses  of  the  Planets. — If  we  arrange  the  planets  according  to 
their  mass,  they  will  stand  in  precisely  the  same  order  as  when 
arranged  according  to  volume,  though  not  in  the  same  proportion. 
The  student  can  verify  this  by  applying  the  principle  explained  in 
Art.  3,  (I.  The  following  table  presents  a  general  view  of  the  com- 
parative masses  of  the  sun  and  planets,  expressed  in  approximate  num- 
bers, the  earth  being  1  :— 


SUN,  . 

.    .  315,000. 

f  Jupiter,  . 

.  301. 

r  Earth,    .    .  1. 

MAJOR 

(Saturn,   . 

.    90. 

TERRESTRIAL  !  Venus,  .    .    \. 

PLANETS. 

Neptune, 

.    16*. 

PLANETS.      1  Mars,     .    .    A- 

Uranus,  . 

.    12*. 

^  Mercury,    .    -fa. 

Moon,  . 

.    •  A. 

QUESTIONS. — 29.  What  is  the  density  of  the  sun  and  moon  ?     a.  Comparative  masses 
of  the  planets  ? 


CHAPTER   IV. 

THE  OBBITAL  REVOLUTIONS  OF  THE  PLANETS. 

30.  A  planet' s  revolution  in  its  orbit  is  sustained  by  the 
united  action  of  two  forces ;  namely,  the  Centripetal  *  and 
the  Centrifugal  \  forces. 

«.  Laws  of  Motion. — No  portion  of  matter  can  set  itself  in  motion ; 
nor,  when  in  motion,  can  it  stop  itself.  Whatever  sets  a  body  in  mo- 
tion, or  stops  it  when  in  motion,  is  called  Force. 

b.  A  body  when  acted  upon  by  a  single  force,  moves  in  a  straight 
line ;  and  will  continue  to  move  in  the  same  direction,  and  with  the 
same  velocity,  until  acted  upon  by  some  other  force. 

Fig.  20. 


*  From  the  Latin  words  centrum,  meaning  the  centre,  and  peto,  meaning 
to  seek. 
t  From  the  Latin  words  centrum,  sundfugio,  meaning  to  Jtee  from. 

QUESTIONS. — 30.  What  forces  sustain  the  planets  in  their  orbits?    a.  What  is  force? 
b.  What  is  th  j  effect  of  a  single  force  ? 


ORBITAL   REVOLUTIONS   OF  THE   PLANETS.        29 

c.  A  force  may  be  either  impulsive,  that  is,  acting  once  and  then 
ceasing  to  act,  or  continuous,  that  is,  acting  constantly. 

d.  Resultant  Motion. — When  a  body  is  impelled  by  two  forces  in 
different,  but  not  opposite,  directions,  it  moves  in  a  straight  line  be- 
tween them.    This  line  is  the  diagonal  of  a  parallelogram  of  which  the 
lines  that  represent  the  two  forces  are  adjacent  sides. 

Thus,  let  A  B  (Fig.  20.)  represent  the  line  over  which  the  body  A  would 
pass  in  a  certain  time  under  the  influence  of  one  force,  and  A  C,  the  line 
over  which  it  would  pass  in  the  same  time,  if  acted  upon  by  another  force ; 
then  under  the  simultaneous  action  of  both  forces,  it  will  pass  over  the  line 
A  D  in  the  same  time,  and  continue  to  move  in  this  line  until  acted  upon  by 
some  third  force.  This  line  is  called  the  resultant  of  the  two  forces. 

e.  Curvilinear  Motion. — If  one  of  the  two  forces  were  a  continuous 
force,  the  body  would  be  drawn,  at  every  point,  from  the  straight  line, 
and,  consequently,  would  move  in  a  curve  line  ;  and  these  two  forces 
might  be  so  related  to  each  other  that  the  body  would  move  around 
the  centre  of  the  continuous  force  in  a  circle  or  ellipse.     In  that  case, 
the  continuous  force  would  be  the  Centripetal  force,  and  the  impulsive 
force,  the  Centrifugal. 

31.  The  CENTRIPETAL  FORCE  is  that  by  which  a  body 
tends  to  approach  the  centre,  or  point  around  which  it  is 
revolving. 

32.  The  CENTRIFUGAL  FORCE  is  that  by  which  a  body 
tends  to  fly  off  from  the  orbit  in  which  it  is  revolving. 

33.  The  centripetal  force  which  acts  upon  the  primary 
planets  is  the  attraction  of  the  sun ;  that  which  acts  upon 
the  secondary  planets  is  the  attraction  exerted  by  their 
respective  primaries. 

34.  All  bodies  attract  each  other  in  direct  proportion  to  the 
mass,  or  quantity  of  matter,  and  inversely  as  the  square  of 
the  distance.    That  is,  a  body  containing  twice  the  quantity 
of  matter  of  another  body  exerts  twice  the  force ;  but,  at 
twice  the  distance,  would  exert  only  one-fourth  the  force. 


QUESTIONS. — c.  What  different  kinds  of  forces?  d.  What  is  the  ei/ect  of  two  forces  / 
Explain  from  the  diagram.  Resultant?  e.  Curvilinear  motion— how  produced  ?  31.  De- 
fine the  centripetal  force,  b'2.  The  centrifugal  force.  i&.  "What  force  acts  on  the 
planets  as  a  centripetal  force  V  34.  State  the  general  law  of  attraction. 


30  THE     ORBITAL     REVOLUTIONS 

a.  Newton's  Discovery. — This  is  the  celebrated  law  of  universal 
gravitation  discovered  by  Sir  Isaac  Newton,  in  1665.  It  is  said  to  have 
been  suggested  to  his  mind  by  the  simple  occurrence  of  an  apple's 
falling  from  a  tree.  Observing  that  all  bodies,  when  unsupported,  fall 
toward  the  centre  of  the  earth,  he  inferred  that  this  must  be  occa- 
sioned by  an  attractive  force  exerted  by  the  earth  ;  and  from  this,  his 
mind  was  led  to  inquire  whether  it  is  not  the  same  force,  that  is,  a 
force  acting  according  to  the  same  law,  which  confines  the  moon  in 
her  orbit  around  the  earth,  and  the  earth  and  planets  in  their  orbits 
around  the  sun.  The  calculations  which  he  made  proved  that  these 
conjectures  were  correct,  and  thus  established  the  law. 

/>.  Centrifugal  Force. — The  centrifugal  force  must  arise  from  an 
impulse  originally  given  to  the  planets  when  they  commenced  their 
motions ;  since,  without  such  an  impulse,  they  would  have  simply 
moved  toward  the  sun  and  have  been  incorporated  with  it.  And  if  the 
centrifugal  force  were  now  destroyed,  the  planets  would  all  move  in 
straight  lines  to  the  sun  ;  while,  if  the  attraction  of  the  sun  were  sus- 
pended, they  would  move  off  into  space  in  tangent  lines  to  their  orbits. 

Let  A  B  (Fig.  20)  represent  the  amount  of  the  centripetal,  and  A  C  that 
of  the  centrifugal  force,  for  a  given  time;  then  completing  the  parallelo- 
gram, and  drawing  the  diagonal  A  D,  we  find  the  point  which  the  body 
when  acted  on  by  both  forces  will  reach  in  that  time.  E,  F,  and  G  may  be 
shown  in  a  similar  way  to  be  the  points  reached  by  the  body  at  the  end  of 
successive  periods  of  time  of  an  equal  length  ;  and  thus,  if  the  forces  acted 
by  impulses,  the  body  would  describe  the  broken  line  formed  by  the  diag- 
onals of  the  parallelograms ;  but  as  the  force  of  gravitation  is  a  continuous 
force,  the  revolving  body  describes  a  curve,  which  may  either  be  a  circle  or 
an  ellipse. 

35.  The  planets'  orbits  are  ellipses,  having  the  sun  or  cen- 
tral body  in  one  of  the  foci. 

a.  Kepler's  Laws. — This  is  the  first  of  the  three  celebrated  truths 
pertaining  to  the  planetary  motions,  discovered  by  Kepler  after  many 
years  of  investigation,  and  announced  by  him  in  1609  ;  hence,  called 
"  Kepler's  Laws."  Previous  to  this  time,  the  general  belief  among 
astronomers  had  been  that  the  planets'  orbits  are  circular  in  form,  since 

QUESTIONS.— a.  By  whom  discovered,  and  how?  6.  Origin  of  the  centrifugal  force  f 
Explain  from  diagram.  35.  What  is  the  shape  of  the  planets'  orhits?  a.  By  whom 
discovered  ?  Previous  belief. 


OF     THE     PLACETS, 


31 


they  conceived  the  circle  to  be  the  most  perfect  and  beautiful  of  curves  ; 
but,  according  to  this  theory,  they  had  found  very  great  difficulty  in 
accounting  for  the  irregularities  in  the  apparent  motions  of  the  planets. 
b.  The  Epicycle.* — This  was,  however,  partially  accomplished 
by  ingeniously  supposing  that  the  planet,  instead  of  revolving  in  a 
simple  orbit,  revolved  in  a  small  circle,  called  an  epicycle,  the  centre 
of  which  moved  around  in  a  circular  orbit.  This  hypothesis  was  in- 
vented, it  is  supposed,  about  two  centuries  B.  C.,  and  was  adopted  by 
Ptolemy  and  all  the  great  astronomers,  including  Copernicus  himself, 
who  could  not  account  for  the  apparent  irregularities  in  the  motions 
of  Mars,  which  has  a  very  eccentric  orbit,  on  any  other  hypothesis. 
The  explanation  by  the  epicycle  is  illustrated  by  the  annexed  diagram. 

The    small  circle    represents  Fig.  21. 

the  epicycle,  the  centre  of  which 
moves  in  the  large  circle  around 
the  sun,  S.  At  A  the  planet  is 
nearest  to  the  sun  ;  but  while  it 
performs  one-quarter  of  a  revo- 
lution in  the  epicycle,  the  latter 
also  moves  over  one-quarter  of 
its  orbit,  and  thus  the  planet  is 
carried  to  B,  and  in  a  similar 
manner  to  C,-its  farthest  point 
from  the  sun,  and  thence  through 
D  to  A  again.  The  difference 
between  its  greatest  distance 
from  the  sun  C  S,  and  its  least 
distance  A  S,  is  equal  to  the  di- 
ameter of  the  epicycle.  KPICTCLB. 

c.  Tycho  Brahe. — Such  ingenious  but  cumbrous  hypotheses  could 
only  be  sustained  by  the  most  imperfect  observations  made  with  the 
rudest  instruments  ;  but  when  astronomy,  as  an  art  of  observation, 
came  to  be  cultivated,  they  were  necessarily  exploded.  Tycho  Brahe 
is  justly  to  be  considered  the  founder  of  modern  practical  astronomy. 
He  was  born  in  1546,  in  Sweden,  and  so  great  a  reputation  did  he 


*  From  the  Greek  words  epi,  meaning  upon,  and  cycle,  a  circle  ;  that  is,  a 
circle  upon  a  circle. 


QUESTIONS. — 6.  What  is  the  hypothesis  of  the  epicycle  ?    Explain  by  the  diagram. 
c.  Tycbo  Brahe  ?    Value  of  his  labors,  and  use  made  of  them  by  Kepler  ? 


32  THE    ORBITAL    REVOLUTIONS 

acquire,  that  Ferdinand,  king  of  Denmark,  built  for  him,  on  an  island 
at  the  mouth  of  the  Baltic,  a  magnificent  observatory,  which  he  styled 
"  Uraniberg.  or  the  City  of  the  Heavens."  His  accurate  observations 
of  the  planets  were  the  means  of  conducting  Kepler  to  the  discovery 
of  his  famous  laws.  No  less  than  nineteen  different  hypotheses  were 
made  by  Kepler,  before  he  could  bring  his  mind  to  abandon  the  theory 
of  the  circular  motion  of  the  planets,  and  then  he  assumed  the  ellipse, 
as  being  the  next  most  beautiful  curve.  The  adoption  of  this  hypo- 
thesis at  once  reconciled  the  computed  with  the  observed  place  of  Mars ; 
and,  on  applying  it  to  the  other  planets,  he  found  still  more  convincing 
proof  of  its  truth. 

36.  The  straight  line  that  joins  the  sun  or  central  body 
with  the  planet  at  any  point  of  its  orbit,  is  called  the  BADIUS- 
VECTOR.* 

37.  The  point  of  a  planet's  orbit  nearest  to  the  sun  is 
called  its  PERIHELION  ;  f  the  point  farthest  from  the  sun,  its 
APHELION.J 

fl.  Apsides. — The  aphelion  and  perihelion  are.  of  course,  the  ex- 
tremities of  the  major  axis.  These  two  points  are  sometimes  called  the 
Apsides,%  and  the  line  that  joins  them,  the  Line  of  Apsides. 

b.  One-half  of  the  sum  of  the  aphelion  and  perihelion  distances  of  a 
planet  is,  of  course,  the  mean  distance.  This  is  always  equal  to  the 
distance  of  a  planet  from  the  sun  when  it  is  at  either  extremity  of  its 
minor  axis.  [See  Introduction,  Art.  29,  &.] 

38.  The  radius-vector  of  a  planet's  orbit  passes  over  equal 
spaces  in  equal  times.    This  is  the  second  of  Kepler's  laws. 

If  8  (Fig.  22)  represent  the  sun  in  the  focus  of  a  planet's  elliptical  orbit,  A 
will  be  the  aphelion,  P  the  perihelion,  and  A  S,  B  S,  C  S,  etc.,  the  radius- 


*  Vector,  in  the  Latin,  means  that  which  carries.     The  radius-vector  is  con- 
ceived to  carry  the  planet  as  it  moves  around  in  its  orbit, 
t  From  the  Greek  peri,  meaning  around  or  near  ;  and  helios,  the  sun. 
J  From  apo,  meaning/rom,  and  helios.    Apo  in  combination  becomes  aph. 
%  Apsis,  plural  apsides,  is  from  the  Greek,  and  means  a  joining. 


QUESTIONS. — 36.  Define  radius-vector.  ST.  Define  perihelion  and  aphelion,  a,  Ap. 
sides  and  apsis  line.  b.  What  is  mean  distance?  33.  What  is  Kepler's  second  law? 
Explain  from  the  diagram. 


OF    THE    PLANETS.  33 

rector  in  different  positions  of  the  plan- 
et. The  planet  moves  in  its  orbit  so 
that  the  spaces  A  S  B,  B  S  C,  etc.,  may 
be  equal,  if  described  in  equal  times. 
It  has  therefore  to  move  much  faster 
in  the  perihelion  than  in  the  aphelion, 
since  at  the  former  point  the  spaces  P 
must  be  wider  in  order  to  make  up 
for  their  diminished  length. 

a.  Orbital    Veloctiy.— The    ve- 
locity of  a  planet  must  therefore  be 

variable  when  it  moves  in  an  ellip-  ELLIPTICAL  OBBIT. 

tical  orbit,  being    greatest   at   the 

perihelion,  least  at  the  aphelion,  and  alternately  increasing  and  dimin- 
ishing between  these  points. 

b.  The  second  law  of  Kepler  is  equally  true  for  every  kind  of  orbit, 
including  ciicular  orbits  ;  but  in  the  latter,  the  radius  of  the  circle 
would  be  the  radius-vector,  and  not  only  would  the  spaces  described 
be  equal,  but  also  the  different  portions  of  the  orbit,  and  consequently, 
the  velocity  would  be  uniform.     The  orbits  of  the  satellites  of  Jupiter 
and  Uranus  are  almost,  if  not  exactly,  circular. 

39.  The  squares  of  the  periodic  times  of  the  planets  are  in 
proportion  to  the  cubes  of  their  mean  distances  from  the 
sun,  or  central  body. 

a.  That  is  to  say,  if  we  square  the  times  which  any  two  planets 
require  to  complete  a  revolution  around  the  sun,  and  then  cube  their 
mean  distances,  the  ratio  of  the  squares  will  be  equal  to  that  of  the 
cubes.    This  law  applies  to  the  secondary  as  well  as  the  primary 
planets. 

b.  History.— This  is  the  third  and  most  celebrated  of  Kepler's  laws. 
It  establishes  a  most  beautiful  harmony  in  the  Solar  System.     In  his 
work  on  "  Harmonics,"  Kepler  first  made  it  known,  with  a  perfect 
burst  of  philosophic  rapture.     "  What  I  prophesied,  twenty-two  years 
ago, — that  for  which  I  have  devoted  the  best  part  of  my  life  to  astro- 
nomical contemplations, — at  length  I  have  brought  to  light,  and  have 

QUESTIONS. — n.  Velocity  of  a  planet — when  variable  ?  6.  When  uniform  ?  39.  Re- 
lation of  periodic  times  to  distances  ?  n.  Is  it  true  of  the  satellites  ?  b.  History  of  its 
discovery  ?  (Repeat  the  three  laws  of  Kepler.) 


34  THE     ORBITAL    REVOLUTIONS 

recognized  its  truth  beyond  my  most  sanguine  expectations.  It  is  now 
eighteen  months  since  I  got  the  first  glimpse  of  light,  three  months 
since  the  dawn  ;  very  few  days  since  the  unveiled  sun,  most  admirable 
to  gaze  on,  burst  out  upon  me.  Nothing  holds  me ;  I  will  indulge 
in  my  sacred  fury.  If  you  forgive  me,  I  rejoice  ;  if  you  are  angry,  I 
can  bear  it.  The  die  is  cast,  the  book  is  written,— to  be  read  either  now 
or  by  posterity,  I  care  not  which  :  it  may  well  wait  a  century  for  a 
reader,  as  God  has  waited  six  thousand  years  for  an  interpreter  of  Ms 
works" 

Sir  John  Herschel  remarks  of  this  law,  "  Of  all  the  laws  to  which 
induction  from  pure  observation  has  ever  conducted  man,  this  thiid 
law  of  Kepler  may  justly  be  regarded  as  the  most  remarkable,  and  the 
most  pregnant  with  important  consequences." 

c.  Demonstration  cf  Kepler's  Laws. — These  laws  were  deduced 
by  Kepler,  as  matters  of  fact,  from  the  recorded  observations  of  him- 
self and  others  ;  but  he  failed  to  show  the  principle  on  which  they  are 
founded,  and  by  which  they  are  connected  with  each  other.     This  was 
reserved  for  Newton,  who,  by  the  discovery  and  application  of  the  law 
of  gravitation,  confirmed  the  truth  of  these  laws  by  exact  mathematical 
reasoning  and  calculation. 

d.  Kepler's  Third  Law  not  quite  true.— The  third  law  is,  how- 
ever, absolutely  correct  only  when  we  consider  the  planets  as  mathe- 
matical points,  without  mass.      Owing  to  the  immense  mass  of  the 
sun,  this  is  relatively  so  nearly  the  fact,  that  the  variation  from  the 
truth  is  very  slight. 

40.  The  eccentricity  of  the  large  planets'  orbits  is  very 
small,  that  of  Mercury  being  the  greatest,  and  Venus  the 
least.  The  orbits  of  the  Minor  Planets  are  generally  remark- 
able for  their  great  eccentricity. 

a.  Comparative  Eccentricities. — The  eccentricity  of  a  planet's 
orbit  is  measured  by  comparing  it  with  one-half  of  the  major  axis. 
The  following  is  an  approximate  statement  of  the  eccentricities  of  the 
large  planets :— Mercury,  £  ;  Mars,  f,,  ;  Saturn,  -fa  ;  Jupiter,  2Jf  ;  Ura, 
nus,  -^  ;  Earth,  -6Lo  ;  Neptune  ,-}T  ;  Venus,  7^5.  The  greatest  of  any 
of  the  minor  planets  is  a  little  over  ^. 


QTTFSTIONS.— c.  By  whom  was  their  truth  mathematically  proved  ?  d.  What  modi- 
fication of  Kepler's  third  law  is  required  ?  40.  What  is  the  amount  of  eccentricity  of 
the  planets'  orbits  ?  a.  State  their  comparative  eccentricities. 


OF    THE     PLANETS. 


35 


The  annexed  diagram  will  aid  in  giv-  Fig.  23. 

ing  the  student  a  correct  idea  of  the 
figure  of  the  planets'  orbits.  This  dia- 
gram represents  an  ellipse,  the  eccentri- 
city of  which  is  £,  or  much  greater  than 
that  of  the  most  eccentric  of  the  minor 
planets.  It  will  be  apparent,  therefore, 
that  the  actual  figure  of  the  planets'  or- 
bits is  but  slightly  different  from  that  of  a 
circle.  If  drawn  on  paper,  the  eye  could 
not  detect  the  difference. 

41.  The  MEAN  PLACE  of  a 
planet  is  that  in  which  it  would 
be  if  it  moved  in  a  circle,  and  of 

course,  with  uniform  velocity ;  the  TEUE  PLACE  is  that  in 
which  it  is  actually  situated  at  any  particular  time. 

42.  The  angular  distance  of  the  true  place  from  the  mean 
place,  measured  from  the  sun  as  a  centre,  is  called  the  Equa- 
tion of  the  Centre. 

Fig.  24. 


ELLIPSE — ECCENTEICITY,     f. 


MEAN  AND  TEUE  PLACES   OF   A    PLANET. 

In  the  above  diagram,  the  ellipse  represents  the  actual  orbit  of  the  planet, 


QUESTIONS.—  41.  What  is  mean  place?    True  place?     42.  Equation  of  the  centre? 
Explain  from  the  diagram. 


36  THE    OKBITAL    KEVOLUTIONS 

and  the  dotted  circle  the  corresponding  circular  orbit.  The  points  marked 
T  represent  the  true  places,  and  those  marked  M,  the  mean  places  of  the 
planet.  As  the  radius-vector  passes  over  greater  portions  of  the  orbit  in 
the  perihelion  than  in  the  aphelion,  the  mean  place  is  before  or  east  of  the 
true  place,  as  the  body  moves  from  aphelion  to  perihelion,  and  behind  or 
west  of  it  in  the  other  half  of  its  revolution.  The  angle  contained  between 
the  radius-vector  and  the  radius  of  the  circle  is  the  equation  of  the  centre. 

43.  The  planets  do  not  all  revolve  around  the  sun  in  the 
same  plane,  but  in  planes  slightly  inclined  to  each  other. 
The  angle  which  the  plane  of  a  planet's  orbit  makes  with 
that  of  the  earth's  orbit  is  called  the  Inclination  of  its 
Orbit. 

44.  Of  all  the  primary  planets,  Mercury  has  the  greatest 
inclination  of  orbit  (7°),  and  Uranus  the  least  (46').     The 
Minor  Planets  are  remarkable  for  a  much  greater  inclination 
of  their  orbits  than  that  of  the  other  planets. 

a.  Since  the  planets'  orbits  are  all  inclined  to  that  of  the  earth,  each 
one  must  cross  the  plane  of  it  in  two  points.  These  two  points  are 
called  the  Nodes  j  one  the  ascending  node,  and  the  other  the  descend 
ing  node. 

Fig.  25. 


B 
INCLINATION   OF  ORBITS. 

Fig.  25  represents  an  oblique  view  of  the  orbits  of  the  earth  and  Venus. 
E  is  the  ascending,  and  F,  the  descending  node.  E  F  the  line  of  nodes, 
and  A  S  G  the  angle  of  inclination  of  the  orbit. 

QUESTIONS.— 43.  What  is  meant  by  inclination  of  orbit  f  44.  Which  planet  has  the 
greatest  ?  Which  has  the  least  ?  Orbits  of  the  Minor  Planets— why  remarkable  ? 


OF    THE     PLANETS. 


37 


45.  The  NODES  *  of  a  planet's  orbit  are  the  two  opposite 
points  at  which  it  crosses  the  plane  of  the  earth's  orbit. 

46.  The  ASCENDING  NODE  is  that  at  which  the  planet 
crosses  from  south  to  north ;  the  DESCENDING  NODE,  that 
at  which  it  crosses  from  north  to  south.    The  straight  line 
which  joins  these  points  is  called  the  Line  of  Nodes. 

Q  is  the  sign  of  the  ascending  node  ;   0 ,  of  the  descending  node. 
Fig.  26. 


INCLINATION   OF  PLANETS'    ORBITS. 

Fig.  26  represents  the  position  of  the  plane  of  each  orbit  in  relation  to 
that  of  the  earth.  The  small  amount  of  deviation  from  one  uniform  plane 
will  be  at  once  apparent.  These  planets,  however,  on  account  of  their  vast 
distance  from  the  sun,  depart  very  far  from  the  plane  of  the  earth's  orbit. 
Thus,  Mars,  although  having  only  2°  of  inclination,  may  be  nearly  5  mil- 
lions of  miles  from  this  plane ;  and  Neptune,  about  85  millions. 


*  From  the  Latin  word  nodus,  meaning  a,  knot. 

QUESTIONS. — 45.  What  are  nodes?    46.  What  is  the  ascending  node?     Descending 
node  ?    Line  of  nodes  ? 


CHAPTER   Y. 

DISTANCES,    PERIODIC    TIMES,    AND   ROTATIONS    OF   THE 
PLANETS. 

47.  The  distances  of  the  planets  from  the  sun  are  so  great 
that  they  can  only  be  expressed  in  millions  of  miles. 

a.  Idea  of  a  Million. — A  million  is  so  vast  a  number  that  we  can 
form  rio  true  conception  of  it  without  dividing  it  into  portions.  To 
count  a  million,  at  the  rate  of  5  per  second,  would  require  about  2|- 
days,  counting  without  intermission,  night  and  day.  A  railroad  car, 
traveling  at  the  rate  of  80  miles  per  hour,  night  and  day,  would  require 
nearly  four  years  to  pass  over  a  million  of  miles.  In  stating  the  dis- 
tances of  the  planets,  the  rate  of  the  express  train  may  be  employed  as 
a  standard  of  comparison,  so  that  the  pupil  may  obtain  something 
more  than  merely  a  knowledge  of  figures  in  learning  these  almost 
inconceivable  distances. 

48.  The  following  are  the  mean  distances  of  the  planets 
from  the  sun,  expressed  in  approximate  round  numbers : — 

Mercury,  .     35  millions.          Jupiter,   .     476  millions. 
Venus,      .     66       "  Saturn,    .      872       " 

Earth,  .    .     9U     "  Uranus,   .  1,754       « 

Mars,   .     .  139*     "  Neptune,    2,746       « 

Minor  Planets,  .  .  260  millions  (average). 
a.  Illustration.— Multiply  each  of  these  numbers  expressing  mil- 
lions by  four,  and  we  shall  find  the  time  which  an  express  train  start- 
ing  from  the  sun  would  require  to  reach  each  of  the  planets.  In  the 
case  of  the  nearest  planet,  this  period  would  be  140  years,  and  of  the 
most  remote,  almost  11,000  years.  A  cannon  ball  moving  at  the  rate 
of  500  miles  an  hour,  would  not  reach  Neptune  in  less  than  623  years. 


QUESTIONS  —  4T.  Distances  of  planets — how  expressed  ?  a.  Idea  of  a  million  ?  48.  State 
the  mean  distances  of  the  primary  planets  from  the  sun.     a.  What  illustration  is  given  ? 


PERIODIC    TIMES    OF    THE    PLANETS.  39 

b.  Bode's  Law. — A  comparison  of  the  distances  given  above  will 
show  a  very  curious  numerical  relation  existing  among  them,  each 
distance  being  nearly  double  that  next  inferior  to  it.  A  more  exact 
statement  of  this  numerical  relation  was  published  in  1772  by  Profes- 
sor Bode,  of  Berlin,  although  not  discovered  by  him :  it  has  usually 
been  designated  "  Bode's  Law."  Take  the  numbers 

0,        3,        6,        12,        24,        48,        96,        192,        384; 
each  of  which,  excepting  the  second,  is  double  the  next  preceding ; 
add  to  each  4,  and  we  obtain 

4,  7,  10,  16,  28,  52,  100,  196,  388; 
which  numbers  very  nearly  represent  the  relative  proportion  of  the 
planets'  distances,  including  the  average  distance  of  the  Minor  Planets. 
In  the  case  of  Neptune,  the  law  very  decidedly  fails,  and,  conse- 
quently, has  ceased  to  have  the  importance  attributed  to  it  previous 
to  the  discovery  of  this  planet  in  1846. 

PERIODIC   TIMES   OF   THE   PLANETS. 

49.  The  following  are  the  periods  of  time  occupied  by  the 
planets  respectively  in  completing  one  revolution  around 
the  sun : — 

Mercury,  .    88  days.  Jupiter,  .    12  yrs.  (nearly.) 

Venus,      .  224.J  "  Saturn,  .    291  " 

Earth, .     .  365J  "  Uranus,  .    84~  " 

Mars,   .    .  1  yr.  322  days.  Neptune,  165     " 

Thus  the  year  of  Neptune  is  about  700  times  as  long  as  that  of 
Mercury. 

50.  Of  all  the  primary  planets,  Mercury  moves  in  its  orbit 
with  the  greatest  velocity,  and   Neptune  with  the  least;  the 
velocities  of   the  planets  diminishing  as  their  distances  from 
the  sun  increase. 

a.  This  is  in  accordance  with  Kepler's  third  law  ;  since  the  ratio  of 
the  periodic  times  increases  faster  than  that  of  the  distances  ;  the  square 

QUESTIONS.— b.  What  is  Bode's  law?  49.  State  the  periodic  times  of  the  primary 
planets.  60.  Which  planet  moves  with  the  greatest  velocity  ?  Which,  the  least  ? 
a.  Why  is  this? 


40  AXIAL    KOTATIONS    OF    THE   .PLANETS. 

of  the  former  being  equal  to  the  cube  of  the  latter.  Thus,  if  the  dis 
tance  of  one  planet  is  four  times  as  great  as  that  of  another,  the 
periodic  time  will  not  be  simply  four  times  as  long,  but  eight  times  as 
long  ;  that  is,  the  square  root  of  the  cube.  (y/43  —  ^/64  =  8).  Hence, 
as  the  planet  has  a  longer  time  in  proportion  to  the  distance  traveled, 
its  velocity  must  be  diminished. 

b.  Comparative  Velocities. — The  following  table  exhibits  the  mean 
hourly  motion  of  the  primary  planets  in  their  orbits  : — 

Mercury,  .     .  104,000  miles.  Jupiter,    .     .  28,700  miles. 

Venus,      .     .     77,000     "  Saturn,     .     .  21,000     " 

Earth,  .     .     .    65,500     "  Uranus,     .     .  15,000     " 

Mars,    .     .    .     53,000     "  Neptune,  .    .  12,000     " 

c.  Illustration. — What  an  amazing  subject  for  contemplation  does 
this  table  present !     For  example,  the  weight  of  the  earth  in  tons  is 
computed  to  be  about  6,000,000,000,000,000,000,000  ;  that  is  to  say,  six 
thousand  million  million  times  a  million,  or  6,000  X  1,000,000  X  1,000,- 
000  X  1,000,000.      Yet   this  body  so    inconceivably   vast  is  rushing 
through  the  abyss  of  space  with  a  velocity  of  1,000  miles  per  minute, 
or  about  15  miles  during  every  pulsation  of  the  heart.     But  the  earth 
in  comparison  with  the  body  around  which  it  is  revolving  is  as  a  single 
grain  of  wheat  compared  with  four  bushels. 

d.  To  find  the  Hourly  Motion. — This  can  be  done  by  the  applica- 
tion of  very  simple  principles.     The  orbits  being  nearly  circles,  twice 
the  mean  distance  will  give  us  the  diameter,  and  3f  times  the  diameter 
will  give  the  circumference,  or  whole  distance  traveled  in  the  periodic 
time.     Then  finding  the  number  of  hours  in  this  time,  and  dividing  the 
whole  distance  by  this  number,  we  obtain  the  hourly  motion.     Thus, 
Mercury's  mean  distance  is  35  million  miles;  then  35X2X3^  =  220 
millions,  the  whole  distance  traveled  in  88  days,  or  88  X  24  =  2112  hours ; 
and  220  million -s- 2112  =  104,166  miles. 

AXIAL   ROTATIONS   OF   THE   PLANETS. 
51.  Besides  revolving  around  the  sun,  the  planets  revolve 
upon  their  axes  in  the  same  direction  as  they  revolve  in 
their  orbits;  that  is,  from  west  to  east.     (See  Art.  18,  a.) 
This  is  called  their  DIUBNAL  KOTATION. 

QUESTIONS. — 6.  State  the  comparative  velocities  of  the  planets.  c.  Illustration  ? 
d.  How  is  the  hourly  motion  in  the  orbit  found  ?  51.  What  is  meant  by  diurnal 
rotation? 


AXIAL    ROTATIONS    OF    THE    PLANETS.          41 

52.  The  Axis  of  a  planet  is  the  imaginary  straight  line 
passing  through  its  centre,  on  which  we   conceive  it  to 
rotate. 

53.  A  planet  must  rotate  with  its  axis  either  perpen- 
dicular or  oblique  to  the  plane  of  its  orbit.     The  axes  of  the 
planets  are  all  considerably  oblique,  excepting  that  of  Jupi- 
ter, which  is  only  3°  from  the  perpendicular ;  that  of  Venus 
is  supposed  to  be  75°. 

54.  The  angle  which  the  axis  of  a  planet  makes  with  a 
perpendicular  to  its  orbit,  is  called  its  INCLINATION  or  Axis. 

Pig.  27. 


INCLINATION   OF  JUPITEB,   EABTH,    AND  VENUS. 

a.  The  inclination  of  the  axis  of  each  planet,  as  far  as  it  has  been 
discovered,  is  as  follows  : — 

Mercury,  .     .  (unknown.)  Jupiter,    .    .    38. 

Venus,      .     .75°.  (?)  Saturn,     .     .  26J?. 

Earth,  .    .     .  23^°,  Uranus,    .     .  (unknown.) 

Mars,   .    .    .  28i°,  Neptune,  .    . 

b.  How  to  Discover  the  Rotation.— The  usual  method  of  dis- 
covering the  rotation  of  a  planet  is  to  examine  the  disc  with  a  powerful 
telescope,  so  as  to  find,  if  possible,  any  spots  upon  it,  and  then  to  detect 
any  regular  movement  of  such  spots  across  the  disc.     Let  the  pupil 
stand  a  short  distance  from  a  terrestrial  globe,  and  let  it  be  caused  to 
revolve,  and  he  will  observe  the  marks  upon  it  move  across,  and  alter- 

QUKBTIONS.— 52.  What  is  the  axis  of  a  planet  ?  53.  Are  the  axes  perpendicular,  or 
oblique  ?  54.  What  is  inclination  of  axis  f  a.  State  the  axial  inclination  of  each 
planet,  b.  How  is  the  axial  rotation  of  a  planet  discovered  ? 


42  AXIAL    ROTATIONS    OF    THE    PLANETS. 

nately  disappear  and  re-appear.    The  same  tiling  must,  of  course,  occur 
in  our  observation  of  the  planets,  if  they  have  a  diurnal  motion. 

55.  The  times  of  rotation  of  the  planets  respectively  are 
as  follows : 

Mercury,  .    .  24}  hours.  Jupiter,     .     .  10  hours. 

Venus,      .    .  23i      "  Saturn,     .     .101    " 

Earth,  ...  24       "  Uranus,    .    .     9^    "  ( ? ) 

Mars,    .    .    .  24A     "  Neptune,      .     (unknown.) 

a.  It  will  be  observed  that  the  terrestrial  planets  all  perform  their 
rotations  in  about  24  hours ;  but  that  the  maj  or  planets  require  less 
than  one-half  that  time. 

b.  Sun's  Rotation. —The  sun  also  rotates  upon  an  axis,  but  requires 
about  608  hours,  or  25  ^   days  to  complete  one  rotation.     The  inclina- 
tion of  its  axis  to  the  plane  of  the  earth's  orbit  is  about  7^°. 


QUESTIONS.— 55.  State  the  time  of  the  rotation  of  each  planet,  a.  What  distinction, 
in  this  respect,  between  major  and  terrestrial  planets  ?  6.  Does  the  sun  rotate  ?  In 
what  time  ? 


CHAPTER  VI. 

ASPECTS    OF    THE    PLANETS. 

56.  The  ASPECTS  of  the  planets  are  their  apparent  posi- 
tions with  respect  to  the  sun  or  to  each  other.    The  principal 
aspects,  that  is,  those  most  frequently  referred  to,  are  Con- 
junction, Quadrature,  and  Opposition. 

57.  A  planet  is  said  to  be  in  CONJUNCTION  with  the  sun 
when  it  is  in  the  same  part  of  the  heavens. 

That  is,   if  the  sun  is  in 
the  east,  the  planet  must  also 
be  in   the  east,  both    being 
seen,  if  visible,  precisely   in 
the  same  direction.     It  is  evi- 
dent that  in  the  case  of  the 
inferior  planets,  this  may  oc- 
cur in  two  ways  ;    namely, 
when  the  planet  is  at  that 
point  of   its  orbit  which  is 
nearest  to  the  earth  or  at  the    \ 
point   most   remote ;    or,    in      \ 
other  words,  when  the  earth    P^\ 
and  planet  are  both  on  the       \ 
same  side  of  the  sun,  or  on 
opposite  sides.    Of  course  a 
superior  planet,  to  be  in  con- 
junction, must  be  on  the  oppo- 
site side  of  the  sun  from  the  earth. 


Fig.  28. 

SUPERIOR  CONJUNCTION 


SUP  R10R 


\ 


INFERIOR 


OPPOSITION 
ASPECTS. 


58.  Conjunction  may  be  Inferior  or  Superior.    Inferior 

QUESTIONS. — 56.  What  is  meant  by  aspects  of  the  planets?    57.  When  is  a  planet 
in  conjunction ?    58.  Of  how  many  kinds  ?    What  is  inferior  conjunction?    Superior  ? 


44  ASPECTS    OF    THE     PLANETS. 

conjunction  is  that  in  which  the  planet  is  between  the  earth 
and  the  sun;  superior  conjunction  is  that  in  which  the 
planet  is  on  the  opposite  side  of  the  sun  from  the  earth. 

59.  A  planet  is  said  to  be  in  OPPOSITION  with  the  sun 
when  it  is  in  the  opposite  part  of  the  heavens. 

a.  That  is,  while  the  sun  is  in  the  east,  the  planet,  if  in  opposition, 
must  be  in  the  west.    If  Jupiter,  for  example,  should  he  rising  just  as 
the  sun  is  setting,  or  vice  versa,  it  would  be  in  opposition.    It  is  obvious 
that  the  superior  planets  only  can  be  in  opposition,  and  that  when  in 
that  position,  they  are  at  the  points  of  their  orbits  nearest  to  the  earth. 

b.  These  different  aspects  obviously  depend  upon  the  angular,  or 
apparent,  distance  of  a  planet  from  the  sun.     [See  Introduction,  Art. 
18,  «].     In  conjunction,  there  is  no  angular  distance,  unless  we  regard 
the  difference  in  the  planes  of  the  orbits  ;  and  when  the  planet  is  in 
conjunction  and  at  either  of  the  nodes,  none  whatever.    In  opposition, 
the  angular  distance  is  180°. 

60.  The  angular  distance  of  a  planet  from  the  sun  is  called 
its  ELONGATION. 

61.  A  planet  is  said  to  be  in  QUADRATURE  when  its  elon- 
gation is  90°. 

a.  The  position  of  quadrature  in  the  heavens  is  half-way  between  con- 
junction and  opposition,  the  planet  being  so  situated  that  the  straight 
lines  that  connect  the  earth  with  the  sun  and  planet,  respectively,  make 
a  right  angle  with  each  other.     Thus  if  a  planet  were  in  quadrature, 
it  would  be  in  the  south,  or  near  it,  either  at  sunset  or  sunrise,  accord- 
ing as  it  were  either  east  or  west  of  the  sun.     It  will  be  obvious,  from 
Fig.  28,  that,  viewed  from  the  earth  as  a  centre,  the  position  of  quad- 
rature  in  the  orbit  is  not  half-way  between  conjunction  and  opposition, 
but  much  nearer  the  latter. 

b.  There  are,  in  all,  five  aspects  of  the  planets,  depending  on  their 
relative  positions.    The  following  are  their  names,  the  angular  dis- 
tances, and  the  characters  used  to  denote  them  : 

QUESTIONS — 59.  When  is  a  planet  in  opposition?  a.  Which  planets  can  be  in  oppo- 
sition? b.  What  is  the  angular  distance  of  a  planet  in  conjunction?  In  opposition? 
60.  What  is  elongation?  61.  Quadrature?  a.  Where  is  quadrature  relatively  to  con- 
junction and  opposition  ?  ft.  Enumerate  and  define  the  five  aspects,  and  write  the  sign 
of  each. 


ASPECTS     OF    THE     PLANETS. 


45 


Conjunction, 
Sextile,  .  . 
Quartile,  .  . 


6         0°. 
*       60°. 

n     90°. 


Trine,    .     . 
Opposition, 


120°. 

180°. 


Fig.  29. 


In  the  diagram,  the  graduated  semicircle  cuts  the  sides  of  all  the  angles 
which  have  their  vertices  at  E,  and  serves  to  measure  the  angular  distance 
of  each  planet  from  the  sun.  V  and  V"  represent  Venus  in  superior  and 
inferior  conjunction,  the  elongation  being,  at  those  points,  0°  ;  while  at  V, 
it  is  at  its  point  of  greatest  elongation.  It  will  be  obvious  from  this  dia- 
gram that  no  inferior  planet  can  be  90°  from  the  sun.  M  represents  Mars 
in  opposition,  and  M'  the  same  planet  in  quadrature.  The  aspect  of  M  and 
V  or  V"  is  opposition  ;  of  M'  and  V  or  V",  quartile. 

62.  The  time  which  elapses  between  two  similar  elonga- 
tions of  a  planet  is  called  its  Synodic  *  Period. 

a.  Thus  the  interval  between  two  successive  conjnnctions  or  oppo- 
sitions is  the  synodic  period.  The  synodic  period  would  be  the  true 
periodic  time  if  the  earth  were  at  rest ;  but  the  earth  is  moving  in  its 
orbit  in  the  same  direction  as  the  planet,  with  a  velocity  less  than  that 


*  From  the  Greek  words  syn,  meaning  together,  and  odos,  which  means  a 
pathway. 

QUESTIONS.— 62.  What  is  the  synodic  period  ?  a.  Why  not  the  true  period  ?  Illus- 
trate by  the  diagram.  How  to  calculate  the  synodic  period  of  the  inferior  planets  ? 
(Fig.  30)  Of  the  superior  planets?  (Fig.  31.) 


4G 


ASPECTS     OF    THE     PLANETS. 


SYNODIC   PEEIOD.      INFEBIOB  PLANETS. 


of  the  inferior  planets  and  greater  than  that  of  the  superior.  Hence, 
the  synodic  period  of  an  inferior  planet  must  always  be  greater  than 
the  periodic  time,  while  that  of  the  superior  planets  is  generally  less. 

Fig-  3O.  The  diagram  represents  Venus  at  V1 

in  inferior  conjunction  with  the  sun,  the 
earth  being  at  E1.  Now  conceive  Venus 
to  move  around  once,  so  as  to  return  to 
V1 ;  the  earth  will  then  have  gone  over 
about  I2f  of  her  orbit,  and  reached  E2, 
and  Venus  will  not  overtake  her  until 
she  reaches  E3,  passing  her  first  position, 
and  hence  making  one  revolution,  and 
the  part  E1  ES  besides,  while  Venus 
makes  two  revolutions,  and  of  course  a 
corresponding  part  of  her  orbit  besides. 
This  part  of  the  orbit  of  each  is  about 
TO  of  the  whole,  in  the  case  of  Venus. 
For  since  Venus  completes  a  revolu- 
tion, or  360°,  in  224*  days,  she  moves 

about  1.6°  per  day;  while  the  earth  moves  about  .98°  per  day ;  hence  Venus 
gains  .62°  per  day;  but  she  has  360°  to  gain,  as  she  leaves  V,  and  300° -*- 
.62°  =582  days.  The  true  synodic  period  is  584  days.  Now,  584  n-224.}  = 
2.6,  number  of  revolutions  of  Venus  during  one  synodic  period  ;  and  584 
-j-  365i  =  1.6,  number  of  revolutions  of  the  earth ;  and  2.6  rev.  —2  rev.  =  Ta5 
rev.rrE1  £3  or  Vi  V3. 

The  synodic  periods  of  the  superior  plan- 
ets, are  illustrated  in  the  annexed  diagram. 
Let  J1  represent  Jupiter  in  opposition,  the 
earth  being  at  E1.  As  Jupiter's  periodic 
time  is  about  12  years,  when  the  earth,  after 
performing  a  revolution,  returns  to  E1, 
Jupiter  has  passed  over  T15  of  its  orbit,  and 
reached  J*,  and  the  earth  moving  a  short 
distance  farther  overtakes  it  at  J3.  In  this 
case,  the  superior  planet  only  moves  over 
a  fraction  of  its  orbit,  while  the  earth  moves 
over  the  same  fraction  of  its  orbit,  and  one 
whole  revolution.  We  can  find  the  synodic 
period  of  Jupiter  from  the  true  period,  in 
SYNODIC  PEHIOD,  supEBioB  pLANET8.tne  f°]l°wmg  manner :— As  Jupiter  per- 
forms only  &  of  a  revolution  while  the 

earth  performs  a  whole  one,  the  earth  gains  H  of  a  revolution,  while  perform- 
ing one  ;  but  to  overtake  Jupiter  when  starting  from  E1,  after  opposition, 


Fig.  31. 


ASPECTS     OF    THE     PLANETS.  47 

she  has  to  gain  an  entire  revolution,  and  1-Hi  =  r?.     Now  £?  of  3654  days 
=  399  days  (nearly) ;  which  is  the  synodic  period  of  Jupiter. 

If  the  periodic  time  of  any  superior  planet  were  exactly  double  that  of 
the  earth,  its  synodic  period  and  periodic  time  would  be  equal.  This  is 
nearly  true  of  Mars  ;  its  periodic  time  being  1  yr.  322  days,  and  its  synodic 
period,  2  yrs.  50  days. 

63.  When  a  planet  appears  in  the  evening,  just  after  sun- 
set, it  is  called  an  Evening  Star  ;  when  in  the  morning,  just 
before  sunrise,  it  is  called  a  Morning  Star. 

a»  The  inferior  planets  being  always  less  than  90°  from  the  sun,  can 
only  appear  as  morning  or  evening  stars.  Mercury  being  a  small 
planet,  and  never  having  but  a  small  amount  of  elongation,  is  a  diffi- 
cult object  to  see  ;  Venus,  being  a  large  planet,  and  having  a  greater 
apparent  distance  from  the  sun,  is  a  very  brilliant  and  beautiful  object, 
either  as  an  evening  or  morning  star.  When  the  former,  her  elonga- 
tion must  of  course  be  east ;  when  the  latter,  west.  The  su}  erior 
planets  are  morning  or  evening  stars  at  different  degrees  of  elongation, 
since  they  may  be  visible  from  sunset  to  sunrise. 

Fig.  32. 


VENTTS   AS  MORNING   AN7>  EVENING  STAB. 

In  the  diagram,  Fig.  32,  Venus  is  represented  as  a  morning  and  evening 

QTTFBTTONS.— 63.  What  is  meant  by  morning  star?     By  evening  star?    a.  What  is 
said  of  the  inferior  planets,  in  this  respect  ?    Explain  fron.  the  diagram. 


48  ASPECTS    OF    THE    PLANETS. 

star.  While  Venus  is  on  the  side  of  the  sun  as  represented  at  V,  she  must 
be  an  evening  star,  since,  as  the  earth  turns,  any  place  at  P  must,  as  it 
turns  from  the  sun  at  the  time  of  sunset,  still  keep  Venus  in  view  by  the 
angular  distance  contained  between  the  lines  drawn  to  the  place  from  the 
sun  and  Venus  respectively ;  but  when  Venus  is  at  V,  the  other  side  of  the 
sun,  the  rotation  of  the  earth  would  bring  Venus  into  view  tit  any  place  as 
P,  before  the  sun.  (The  student  should  carefully  notice  the  direction  of 
the  motion  as  indicated  by  the  arrows.)  Venus,  of  course,  remains  the 
same  side  of  the  sun  during  one-half  of  the  synodic  period,  or  292  days. 

QUESTIONS    FOE    EXEKCISE. 

1.  When  a  planet  is  in  quadrature,  what  is  its  elongation  ? 

2.  What  is  its  elongation  when  in  inferior  conjunction  ? 

3.  What  is  its  elongation  in  superior  conjunction  ? 

4.  How  many  degrees  of  elongation  has  it  when  in  opposition  ? 

5.  Which  of  the  planets  can  be  in  inferior  conjunction  ? 

6.  Which  can  be  in  superior  conjunction  ? 

7.  Which,  can  be  in  opposition  ? 

8.  Which  can  be  in  quadrature  ? 

9.  Can  the  elongation  of  Mercury  or  Venus  exceed  90°  ? 

10.  Can  that  of  Jupiter  ? 

11.  What  is  the  greatest  elongation  of  a  superior  planet  ? 

12.  When  Venus  is  in  inferior  conjunction,  and  Mars  in  opposition, 
what  is  their  angular  distance  from  each  other  ?    [See  Fig.  29.] 

18.  What  is  their  angular  distance  when  Venus  is  in  inferior  con- 
junction, and  Mars  in  superior  conjunction  ? 

14.  How  many  degrees  are  they  apart  when  Venus  is  in  superior 
conjunction  and  Mars  is  in  quadrature  ? 

15.  When  the  elongation  of  Venus  is  30°,  and  that  of  Mars  is  120°, 
what  is  their  angular  distance  from  each  other  ? 

16.  If  Venus  is  50°  from  Mars,  and  the  latter  body  is  in  quadrature, 
what  is  the  elongation  of  Venus  ? 


CHAPTER   VII. 

THE    EARTH. 

64.  That  the  earth  is,  in  its  general  form,  a  spherical  body, 
is  plainly  indicated  by  a  few  simple  facts  : 

1.  Navigators  are  able  to  sail  entirely  around  it  either  in 
an  eastward  or  a  westward  direction  ; 

2.  The  earth  and  the  sky  always  seem  to  meet  in  a  circle, 
when  the  view  is  unobstructed  ; 

3.  The  top  of  a  distant  object  always  appears  above  this 
circle,  before  the  lower  parts  ;  as  the  sails  of  a  ship  before 
its  hull  ; 

4>  The  elevation  of  the  spectator  causes  this  circle  to  sink, 
so  as  to  show  more  of  the  earth's  surface,  and  equally  on 
all  sides  ; 

5.  The  apparent  movements  of  the  heavenly  bodies 
around  the  earth,  some  in  large  circles,  some  in  small  circles  ; 
one  particular  star  in  the  heavens  not  appearing  to  have 
any  motion  at  all. 

a.  This  last  circumstance  is  accounted  for  by  supposing  that  the 
earth's  axis  points  to  this  star.  Hence  it  is  called  the  North,  or  Pole  Star. 

/>.  The  first  practical  proof  that  the  earth  is  spherical  was  afforded 
by  the  voyage  of  Magellan,  whose  squadron,  in  1519-22,  sailed  entirely 
around  the  earth. 

SECTION    I. 

LATITUDE   AND   LONGITUDE. 

65.  Points  are  located  upon  the  surface  of  the  earth  by 
measuring  their  distances  from  certain  established  circles 


What  five  circumstances  indicate  that  the  general  form  of  the  earth 
is  spherical  ?  a.  What  is  the  north  star  ?  65.  How  are  points  located  on  the  earth's 
Surface. 


50  LATITUDE    AND     LONGITUDE. 

conceived  to  be  drawn  upon  it.  The  position  of  these  cir- 
cles is  determined  by  their  relation  to  two  fixed  points, 
called  the  POLES. 

66.  The  poles  are  the  two  extremities  of  the  earth's  axis, 
one  being  called  the  NORTH  POLE,  and  the  other  the  SOUTH 
POLE. 

a.  As  the  earth  turns  on  its  axis  from  west  to  east,  it  causes  all  the 
other  heavenly  bodies  to  seem  to  revolve  around  it  from  east  to  west, 
in  circles  contracting  in  size  towards  the  fixed  point  of  the  heavens, 
called  the  celestial  pole,  near  which  is  the  pole-star.  The  celestial 
poles  correspond  to  the  poles  of  the  earth,  being  the  two  points  at  which 
the  earth's  axis,  if  extended,  would  meet  the  sphere  of  the  heavens. 

67.  The  great  circle  exactly  midway  between   the  two 
poles  is  called  the  EQUATOR.     Its  plane  divides  the  earth 
into  northern  and  southern  hemispheres. 

68.  The  great  circles  that  pass  through   the  poles  are 
called  meridian  circles  ;  the  half  of  a  meridian  circle  that 

Fig.  33.  extends  from  pole  to  pole,  is  called  a  Me- 

Meridian  ™^ 

a.  Meridian  circles  must,  of  course  be  per- 
pendicular to  the  equator  and  the  plane  of  any 
one  of  them  would  divide  the  earth  into  eastern 
and  western  hemispheres.  A  great  circle  that 
is  perpendicular  .to  another  is  sometimes  called 
a  secondary  to  it.  Thus  the  meridian  circles 
are  secondaries  to  the  equator. 

69.  The  position  of  a  place  on  the  surface  of  the  earth  is 
indicated  by  its  latitude  and  longitude.     LATITUDE  is  dis- 
tance north  or  south  from  the  equator  ;  LONGITUDE,  distance 
east  or  west  from  some  established  meridian,  called  a  First, 
or  Prime,  Meridian. 


66.  What  are  the  poles  ?  n.  What  are  the  celestial  poles?  67.  What  is 
the  equator?  68.  What  are  meridian  circles?  Meridians?  n.  Their  relation  to  the 
equator?  What  is  a  secondary  ?  69.  What  is  latitude  ?  Longitude? 


LATITUDE    AND    LONGITUDE.  51 

Pig.  34.  70.  Small  circles  parallel  to  the  equa- 

tor  are  called  PARALLELS  OF  LATITUDE. 
71.  Latitude  is  reckoned  on  a  meridian, 
from  the  equator  to  the  poles ;  longitude 
is  reckoned  from  the   prime  meridian 
round  to  the  opposite  meridian. 

a.  Distance  from  any  great  circle  must  be 
reckoned  on  a  secondary  to  that  circle.  It 
will  be  easily  perceived  by  the  pupil  that  the  poles  have  the  greatest 
possible  latitude— namely,  90°  ;  and  that  places  situated  under  the  me- 
ridian opposite  the  prime  meridian,  have  the  greatest  longitude,  or 
180°  east  or  west ;  also,  that  a  place  situated  at  the  intersection  of  the 
prime  meridian  with  the  equator  can  have  neither  longitude  nor 
latitude. 

b.  Difference  of  Time. — Difference  of  Longitude  causes  difference 
of  time.    Since  the  earth  turns  toward  the  east,  any  place  east  of 
another  place,  must  have  later  timey  because  it  is  sooner  carried,  by  the 
motion  of  the  earth,  under  the  sun  ;  and,  as  an  entire  rotation,  or  360°, 
is  performed  in  24  hours,  15°  of  longitude  must  be  equivalent  to  one 
hour  of  time.    Thus,  London  is  74°  east  of  New  York  ;  and,  conse- 
quently, when  it  is  noon  at  New  York,  it  is  5  o'clock  in  the  afternoon 
at  London,  the  sun  having  passed  the  meridian  five  hours  earlier. 

c.  Difference  of  Longitude  may  be  converted  into  Difference 
of  Time,  by  multiplying  the  degrees  and  minutes  by  4  ;  the  former  of 
which  will  then  be  minutes  of  time ;  and  the  latter,  seconds.    For 
since  ,J5  the  number  of  degrees  is  equal  to  the  number  of  hours,  f  £,or 
4  times,  the  degrees  must  be  equal  to  the  minutes  ;  and,  for  the  same 
reason,  4  times  the  minutes  of  space  must  be  equal  to  seconds  of 
time. 

(I.  To  convert  Difference  of  Time  into  Difference  of  Longitude, 
reduce  the  hours  to  minutes,  and  divide  by  4.  For  since  15  times  the 
hours  are  equal  to  the  degrees,  /0-  of  15,  or  {,  the  minutes  must  be 
equal  to  the  degrees. 


QUKSTIONS.— 70.  What  are  parallels  of  latitude  ?  71.  How  are  latitude  and  longitude 
reckoned?  a.  Where  is  the  latitude  greatest  ?  The  longitude?  What  point  or  place 
on  the  earth's  surface  has  neither  latitude  nor  longitude  ?  fo.  How  does  difference  of 
longitude  cause  difference  of  time?  r.  How  to  convert  diff-rcnce  of  longitude  into 
difference  of  time?  rf.  How  to  convert  difference  of  time  into  difference  of  longitude. 


LATITUDE     AND     LONGITUDE. 


PROBLEMS   FOR   THE   GLOBE. 

PROBLEM  I. — To  find  the  latitude  and  longitude  of  a 
place :  Bring  the  given  place  to  the  graduated  side  of  the 
brass  meridian  [the  circle  of  brass  that  encompasses  the 
globe],  which  is  numbered  from  the  equator  to  the  poles : 
and  the  degree  of  the  meridian,  over  the  place  will  be  the 
latitude ;  and  the  degree  of  the  equator,  under  the  meridian, 
east  or  west  of  the  prime  meridian,  will  be  the  longitude. 

Verify  the  following  by  the  globe  : 

LAT.  I,ONG. 

LONDON,  .    .    .  5U°  N. ;    0°. 
PARIS,      .    .     .  49°    N. ;    2^°  E. 
WASHINGTON,  .  39°    N. ;  77°    W. 
CINCINNATI,     .  39°    N. ;  84£°  W. 


C.  GOOD  HOPE,  34°  S. ;  18^°  E. 
BERLIN,  .  .  52£0  N. ;  13^°  E. 
MADRAS,  .  .  13°  N. ;  80°  E. 
SANTIAGO,  .  .  32F  S. ;  70|°  W. 


PROBLEM  II. — The  latitude  and  longitude  of  a  place 
being  given,  to  find  the  place :  Find  the  degree  of  longitude 
on  the  equator,  bring  it  to  the  brass  meridian,  and  under 
the  given  degree  of  latitude,  on  the  meridian,  will  be  the 
place  required. 

EXAMPLES. 

1.  What  place  is  in  lat.  30°    N.,  and  long.  90°  W.  ?  Am.  New  Orleans 

2.  What  place     "      "    42 \°  N.,  "      71°  W.?  An*.  Boston. 

3.  What  place     "      "    40f  N.,  "      74°  W.  ?  Ana.  New  York. 

PROBLEM  III. — To  find  the  difference  of  latitude  or  Ion 
gitude  between  any  two  places  :  Find  the  latitude  or  longitude 
of  both  places ;  if  on  the  same  side  of  the  equator  or  merid- 
ian, subtract  one  from  the  other ;  if  on  different  sides,  add 
them ;  the  result  will  be  the  answer  required. 

EXAMPLES. 

Find  the  difference  of  latitude  and  longitude  of 

\.  London  and  Naples.  Am.  Lat.  10^°,  long.  14£8. 

2.  New  York  and  San  Francisco.     Ans.  Lat.    3°,    long.  58./°- 

3.  Stockholm  and  Rio  Janeiro.        Ans.  Lat.  82°,    long.  61°. 


LATITUDE    AND    LONGITUDE.  53 

PROBLEM  /F. — To  find  all  the  places  that  have  the  same 
latitude  as  any  given  place :  Bring  the  given  place  to  the 
brass  meridian,  and  observe  its  latitude ;  turn  the  globe 
round,  and  all  places  that  pass  under  the  same  degree  of  the 
meridian  will  be  those  required. 

EXAMPLES. 

What  places  have  the  same,  or  nearly  the  same,  latitude  as 

1.  MADRID?     Ana.  Minorca,  Naples,   Constantinople,   Kokand,   Salt 

Lake  City,  Pittsburgh,  New  York. 

2.  HAVANA  ?     Ans.  Muscat,  Calcutta,  Canton,  C.  St.  Lucas,  Mazatlan. 

PROBLEM  V. — To  find  the  places  that  have  the  same  longi- 
tude as  any  given  place :  Bring  the  given  place  to  the  grad- 
uated side  of  the  brass  meridian,  and  all  places  under  the 
meridian  will  be  those  required. 

EXAMPLE 

What  places  have  the  same,  or  nearly  the  same,  longitude  as 
LONDON  ?    Ans.  Havre,  Bordeaux,  Valencia,  Oran,  Gulf  of  Guinea. 

PROBLEM  VL — A  time  and  place  being  given,  to  find 
what  o'clock  it  is  at  any  other  place :  Bring  the  place  at  which 
the  time  is  given  to  the  brass  meridian,  set  the  index  to  the 
given  time,  and  turn  the  globe  till  the  other  place  comes  to 
the  meridian,  and  the  index  will  point  to  the  time  required. 

NOTE. — If  the  place  be  east  of  the  given  place,  turn  the  globe  westward ; 
if  west,  turn  it  eastward. 

This  problem  can  be  performed  without  the  globe  by  finding  the  differ- 
ence of  longitude,  as  indicated  in  Art.  71,  c,  d. 

EXAMPLES. 

1.  When  it  is  noon  at  New  York,  what  o'clock  is  it  at  London  ? 

Ans.  5  o'clock  P.M.  (nearly). 

2.  When  it  is  10  o'clock  A.M.  at  St.  Petersburg,  what  o'clock  is  it  at 

the  City  of  Mexico  ?    Ans.  1  hour  20  min.  A.M. 

3.  When  it  is  9  o'clock  P.M.  at  Rome,  what  o'clock  is  it  at  San  Fran- 

cisco?   Ans.  Noon. 


54  THE     HORIZON. 

PROBLEM  VII. — To  find  the  distancce  between  any  two 
places :  Lay  the  graduated  edge  of  the  quadrant  over  both 
places,  so  that  the  division  marked  0  may  be  on  one  of  them ; 
and  the  number  of  degrees  between  them,  reduced  to  miles, 
will  be  the  distance  required. 

NOTE.— If  geographic  miles  are  required,  multiply  the  degrees  by  CO;  if 
statute  miles,  by  091. 

EXAMPLES. 

Find  the  distance  in  geographic,  and  statute  miles  between 

1.  NORTH  CAPE  and  CAPE  MATAPAN.    Am.  2,100  geog.  miles  ;  2,413f 

statute  miles. 

2.  Rio  JANEIRO  and  CAPE  FAREWELL.  Ans.  4,980  geog.  miles  ;  5,736  j 

statute  miles. 

SECTION    II. 

THE    HORIZON. 

72.  The  HORIZON  *  OF  A  PLACE  is  the  circle  which  sepa- 
rates the  visible  part  of  the  heavens  from  the  invisible. 

(i.  The  surface  of  the  earth  appears,  to  a  person  standing  upon  it, 
like  a  great  plane,  extending  equally  on  all  sides,  and  limited  by  a  cir- 
cle at  which  the  earth  and  sky  appear  to  meet.  As  the  elevation  of 
the  spectator  increases,  the  greater  is  the  extent  of  surface  embraced 
within  this  circle,  and  the  more  extensive  the  visible  heavens  as  com- 
pared with  the  invisible,  On  the  other  hand,  an  eye  situated  exactly 
on  the  earth's  surface  sees  but  a  point  of  it,  but  still  beholds  a  circle 
bounding  the  visible  heavens,  the  plane  of  which  would  touch  the 
earth's  surface  at  the  exact  point  where  the  eye  is  located.  This  circle 
is  called  the  Sensible  or  Visible  Horizon  ;  and  the  depression  of  it,  due 
to  the  elevation  of  the  spectator,  the  Dip  of  the  Horizon.  The  follow- 
ing definitions  may  therefore  be  given  of  each  : 

73.  The  SENSIBLE  HORIZON  is  that  circle  of  the  celestial 


*  From  the  Greek  word  horizo,  meaning  to  bound. 

QUESTIONS. — 72.  What  is  the  horizon  of  a  place  ?    a.  General  phenomena  connected 
with  the  horizon  ?    73.  What  is  the  sensible  horizon  ? 


THE     HORIZON. 


55 


sphere  the  plane  of  which  touches  the  earth  at  the  place  of 
the  spectator. 

a.  By  the  Celestial  Sphere  is  meant  the  concave  sphere  of  the  heavens, 
in  which  the  heavenly  bodies  appear  to  be  placed,  the  observer  being 
at  the  centre  within,  and  looking  upward. 

74.  The  DIP  OF  THE  HORIZOX  is  the  depression  of  the 
sensible  horizon  caused  by  the  elevation  of  the  spectator, 
and  bringing  a  circular  portion  of  the  earth's  surface  into 
view. 

In  the  diagram,  let  the  small  circle 
whose  centre  is  E,  represent  the 
earth,  the  portion  of  the  large  circle 
V  Z  V  a  part  of  the  celestial  sphere, 
and  P  the  point,  or  place,  of  the  spec- 
tator. Then  the  tangent  S  P  S  will 
represent  the  plane  of  the  sensible 
horizon,  and  S  Z  S  the  visible  heavens. 
Conceive  the  observer  to  stand  above 
the  surface  at  II ;  the  tangents  H  V 
and  II  V'  will  then,  at  their  points  of 
contact,  D  and  D,  limit  the  visible 
part  of  the  earth's  surface,  and  at 
their  extremities,  V  and  V7,  the  visi- 
ble heavens.  S  V  or  S  V  will  be,  of  course,  the  dip  of  the  horizon.  At  the 
point  P,  the  visible  part  of  the  heavens  is  less  than  the  invisible  ;  but  at  so 
great  an  elevation  as  H  P  (represented  as  about  1,000  miles),  the  visible 
part  would  be  much  greater  than  the  invisible,  and  a  large  part  of  the 
earth's  surface,  denoted  by  the  arc  D  D,  would  come  into  view.  The  dip, 
however,  at  any  attainable  height  is  very  small,  and  only  an  inconsiderable 
portion  of  the  earth's  surface  can  ever  be  seen.  The  line  R  R  represents  the 
plane  of  a  great  circle,  which  divides  the  celestial  sphere  into  equal  parts, 
passing  through  the  centre  of  the  earth,  and  situated  at  a  distance  from 
the  plane  of  the  sensible  horizon  equal  to  the  semi-diameter  of  the  earth, 
or  nearly  4,000  miles. 

75.  The  great  circle  of  the  celestial  sphere  which  is  paral- 
lel to  the  sensible  horizon,  is  called  the  RATIONAL  HORIZON. 


SENSIBLE  AND  BATIONAL  HORIZON. 


QUFSTIONS.— a.  What  is  meant  by  the  celestial  sphere  f    74.  What  is  the  dip  of  the 
horizon  t     Explain  by  the  diagram.    75.  What  is  the  rational  horizon  ? 


56  THE    HORIZON. 

It  divides  the  earth  and  the  celestial  sphere  into  upper  and 
lower  hemispheres. 

The  terms  upper  and  lower,  above  and  below,  and  the  like,  are  only 
applicable  to  the  horizon.  The  rational  horizon  is  the  real  horizon  ; 
it  is  the  standard  circle  for  referring  the  apparent  positions  of  all  the 
heavenly  bodies. 

76.  The  poles  of  the  horizon  are  called  the  ZENITH  and 
the  NADIR.    The  zenith  is  the  point  directly  overhead ;  the 
nadir  is  the  point  opposite  to  the  zenith,  and  directly  under 
our  feet. 

The  one  is  the  pole  of  the  visible,  or  upper,  hemisphere  ;  the  other, 
the  pole  of  the  invisible,  or  lower.  Each  is,  of  course,  90°  from  the 
horizon. 

77.  Great  circles  conceived  to  pass  through  the  zenith  and 
nadir  are  called  VERTICAL  CIRCLES,  or  VERTICALS. 

a.  Vertical  circles,  being  perpendicular  to  the  horizon,  are  secondaries 
to  it.  The  position  of  a  body  in  the  celestial  sphere  is  defined  by  its 
distance  from  the  rational  horizon,  and  some  selected  vertical  circle  ; 
just  as  the  position  of  a  place  on  the  earth's  surface  is  determined  by 
its  latitude  and  longitude.  The  vertical  selected  for  this  purpose  is 
that  which  the  centre  of  the  sun  reaches  and  passes  at  noon.  This 
circle,  of  course,  passes  through  the  north  and  south  points  of  the 
horizon,  and  also  through  the  celestial  poles,  its  plane  intersecting  the 
earth  so  as  to  form  a  terrestrial  meridian.  It  is  therefore  called  the 
Meridian  of  flie  Place. 

78.  The  MERIDIAN   OF  A  PLACE  is  the  vertical  circle 
which  passes  through  the  north  and  south  points  of  the 
horizon  of  that  place.     It  divides  the  celestial  sphere  into 
eastern  and  western  hemispheres. 

a.  When  a  body  is  on  the  meridian,  it  is  said  to  culminate,  because 
it  is  at  that  time  at  its  greatest  distance  above  the  horizon  during 
24  hours. 


QUESTIONS.— 76.  What  are  the  zenith  and  the  nadir  ?  11.  What  are  vertical  circles  ? 
a.  How  is  the  position  of  a  body  in  the  celestial  sphere  defined  ?  78.  What  is  the  me- 
ridian of  a  place  ?  a.  When  is  a  body  said  to  culminate  ? 


THE     H  O  It  I  Z  0  N  . 


57 


79.  The  distance  of  a  body  above  the  horizon  is  called  its 
ALTITUDE.    It  is  reckoned  on  a  vertical  circle,  from  the 
horizon  to  the  zenith. 

At  the  horizon,  therefore,  the  altitude  is  0°  ;  at  the  zenith,  90°. 

80.  The  distance  of  a  body  east  or  west  from  the  meridian 
is  called  its  AZIMUTH.    It  is  reckoned  on  the  horizon. 

a.  Prime  Vertical  5  Amplitude. — The  altitude  and  azimuth  of  a 
body  would  be  sufficient  to  define  its  position  in  the  visible  heavens  ; 
but  astronomers  sometimes  employ  another  vertical  as  a  standard  of 
reference,  namely,  that  which  passes  through  the  east  and  west  points 
of  the  horizon,  cutting  the  meridian  at  right  angles.  This  is  called 
the  Prime  Vertical ;  and  the  distance  of  a  body  from  it,  north  or  south, 
is  call  the  Amplitude.  These  are,  at 
present,  but  little  used.  By  the  am- 
plitude of  the  sun  is  generally  meant 
the  distance  at  which  it  rises  from 
the  east,  or  sets  from  the  west  point 
of  the  horizon. 

In  the  diagram,  let  N  E  S  W  repre- 
sent the  rational  horizon,  the  circle 
passing  through  N  S,  the  meridian,  and 
that  passing  through  E  W,  the  prime 
vertical ;  then  if  A  be  the  position  of 
the  sun  at  rising,  A  E  will  represent  its 
amplitude,  and  A  N,  its  azimuth ;  the 
altitude  being  Oc. 


Sadir 


81.  The  ZENITH  DISTANCE  of  a  body  is  its  distance  from 
the  zenith  reckoned  on  a  vertical  circle. 

The  zenith  distance  is  the  complement  of  the  altitude,  that  is,  the 
difference  between  it  and  90°. 

82.  The  circles  which  the  heavenly  bodies  may  be  con- 
ceived to  describe  during  their  apparent  daily  revolution 
around  the  earth,  are  called  CIRCLES  OF  DAILY  MOTION. 

QUESTIONS. — 79.  What  is  altitude?  80.  Azimuth?  a.  What  is  the  prime  vertical  ? 
What  is  amplitude?  81.  What  is  zenith  distance?  82.  What  are  circles  o*  daily 
motion  ? 


58 


THE    HORIZON. 


Fig.  37. 
Parallel  Sphere 


JSadir 


Pig.  38. 

Right  Sphere 
Zemtfc 


Pole 


-Nadir 

Fig.  39. 
Oblique  Sphere 


a.  Positions  of  the  Sphere. — The  circles  of 
daily  motion  are  parallel,  perpendicular,  or  ob- 
lique to  the  horizon,  according  to  the  place  of  the 
observer  upon  the  surface  of  the  earth.     When 
standing  exactly  at  either  of  the  poles,  he  would 
have  the  celestial  pole  in  the  zenith,  and  the 
circles  of  daily  motion  would  be  parallel  to  the 
horizon  ;  this  position  is  called  a  Pan  allel  Sp7iere. 
At  the  equator,  the  celestial  poles  would  be  in  the 
horizon,  and  the  circles  of  daily  motion  perpen- 
dicular to  it ;  this  position  is  called  a  Right 
Sphere.    At  any  place  between  the  equator  and 
the  pole  the  circles  would  be  oblique 
to  the  horizon,  and  the  pole  would  be 
raised  to  an  altitude  equal  to  the  lati- 
tude of  the  place ;   this  is  called  an 
Oblique  Sphere. 

It.  In  a  parallel  sphere,  one-half  of  all 
the  circles  of  daily  motion  are  wholly 
above  the  horizon,  and  the  heavenly 
bodies  do  not  appear  to  rise  and  set, 
but  to  move  around  in  parallel  circles 
contracting  in  size  toward  the  zenith  ; 
in  a  right  sphere,  all  the  circles  are 
divided  equally  by  the  horizon,  there 
being  as  much  of  each  above  as  below  it ; 
in  an  oblique  sphere,  some  of  the  circles  of 
daily  motion  are  wholly  above  the  horizon, 
others  wholly  below  it,   and  all  between 
these,  divided  unequally  by  it.      All   this 
will  be  rendered  apparent  by  the  accompa- 
nying diagrams. 

83.  The  circle  of  an  oblique  sphere 
in  which  the  stars  never  set  is  called 
the  CIRCLE  OF  PERPETUAL  APPARI- 


Pole 


QUFSTIONS.— ft.  What  are  the  three  positions  of  the  sphere  ?  Define  each.  ft.  TTow 
are  the  circles  of  daily  motion  divided  by  the  horizon  in  each?  83.  What  is  the  circle 
of  perpetual  apparition  ?  Of  perpetual  occultation  ? 


PARALLAX. 


59 


TION  ;  that  in  which  they  never  rise,  the  CIRCLE  OF  PER- 
PETUAL OCCULTATION. 

84.  That  part  of  a  circle  of  daily  motion  which  is  above 
the  horizon,  and  which  a  body  describes  from  its  rising  to 
its  setting,  is  called  the  DIURNAL  ARC  ;  the  part  below  the 
horizon  is  called  the  NOCTURNAL  ARC. 

In  the  diagram  of  the  oblique  sphere  (Fig.  39),  H  H  represents  the  ra- 
tional horizon,  Z  and  N  the  zenith  and  nadir,  P  P  the  poles,  E  E'the  equa- 
tor extended  to  the  heavens,  and  the  dotted  lines,  circles  of  daily  motion. 
Then  Z  E  will  be  the  same  number  of  degrees  as  the  latitude,  E  H  will  be 
the  altitude  at  which  the  equinoctial  or  equator  intersects  the  meridian, 
and  P II  will  be  the  altitude  of  the  celestial  pole.  Now  E  P  is  equal  to  Z  H, 
each  being  90° ;  hence,  by  subtracting  Z  P  from  each,  we  find  E  Z  =  P  H  ; 
that  is,  the  altitude  of  the  pole  equal  to  the  latitude. 


PARALLAX. 

85.  The  TRUE  ALTITUDE  of  a  body  is  the  distance  at 
which  it  would  appear  to  be  from  the  horizon,  if  it  could  be 
viewed  from  the  centre  of  the  earth. 

In    the    diagram    let    the  Fig.  4O. 

email  circle  represent  the 
earth,  having  its  centre  at  E ; 
A,  B,  and  C,  a  body  as  seen  at 
different  altitudes  from  the 
place,  P ;  E  H,  the  plane  of 
the  rational  horizon ;  P  h,  the 
plane  of  the  sensible  horizon, 
and  E  Z,  the  direction  of  the 
zenith.  At  A,  the  body  being 
in  the  sensible  horizon,  its  ap- 
parent altitude  will  be  noth- 
ing ;  but  if  viewed  from  E,  it 
would  appear  to  be  above  the 
horizon  a  distance  equal  to  the 
angle  mE  H,  or  its  equal  m  A  h, 
since  the  difference  in  direction  between  the  lines  E  H  or  Ph,  and  E  m  is  the 
difference  between  the  apparent  and  true  altitude.  At  B,  there  is  evidently 


QUESTIONS. — 84.  Define  diurnal  arc,  and  nocturnal  arc. 
is  the  true  altitude  of  a  body? 


Explain  Fig.  39.    85.  What 


60  PARALLAX. 

a  less  difference  of  direction  between  the  lines  P  n  and  E  o,  and  when  the 
body  is  at  C,  the  centre  of  the  earth,  the  place  of  the  observer,  and  the  po- 
sition of  the  body  being  all  on  the  same  straight  line,  the  true  is  the  same 
as  the  apparent  altitude.  It  is  evident  that  the  apparent  altitude  is  always 
less  than  the  true  altitude,  except  when  the  body  is  seen  in  the  zenith,  as  at 
C  ;  and  that  there  is  the  greatest  difference  when  the  body  is  in  the  horizon, 
as  at  A. 

86.  The  difference  between  the  true  and  apparent  altitude 
of  a  heavenly  body  is  called  its  PARALLAX. 

87.  The  parallax  of  a  body  is  greatest  when  it  is  in  the 
horizon,  and  diminishes   towards  the  zenith,  where   it  is 
nothing.     The  parallax  of  a  body  when  in  the  horizon  is 
called  its  Horizontal  Parallax. 

In  the  preceding  diagram,  the  angle  m  A  h,  or  its  equal  P  A  E,  is  called 
the  angle  of  parallax,  o  B  n,  or  P  B  E,  is  the  angle  of  parallax  for  the  posi- 
tion B.  The  angular  distance  of  the  sensible  and  rational  horizons  is,  of 
course,  the  horizontal  parallax. 

a»  The  greater  the  distance  of  a  body  from  the  earth,  the  smaller  is 
the  angle  of  parallax. 

Fig.  41.  Thus  the  horizon- 

tal parallax  of  a  body 
at  A,  (Fig.  41.)  is  A  E 
H,  or  P  A  E ;  but  at 
B,  it  is  the  smaller 
angle  B  E  H,  or  P  B  E.  The  horizontal  parallax  of  any  body  is  really  the 
angle  subtended  by  the  semi-diameter  of  the  earth  at  the  distance  of  the 
body  ;  and,  of  course,  the  greater  the  distance,  the  smaller  the  angle. 

6.  The  horizontal  parallax  of  the  moon  is  nearly  1°  ;  that  of  the 
sun,  less  than  9".  In  a  subsequent  chapter,  it  will  be  shown  that 
by  finding  the  parallax  of  a  body,  we  can  determine  its  distance  from 
the  earth. 

88.  Since  the  apparent  altitude  of  a  body  is  less  than  the 
true  altitude  by  the  amount  of  parallax,  the  effect  of  paral- 
lax is  said  to  be  to  diminish  the  altitude.     The  apparent 

QUESTIONS.— 86.  What  is  parallax?  87.  Where  is  it  greatest?  What  is  horizontal 
parallax?  Explain  Fig.  41.  a.  What  relation  between  the  distance  of  a  body  and  its 
parallax  ?  Explain  by  the  diagram,  b.  What  is  the  horizontal  parallax  of  the  moon 
and  sun  ?  88.  What  is  the  effect  of  parallax  ? 


REFRACTION.  61 

altitude  is  therefore  corrected  by  adding  the  amount  of 
parallax  due  to  the  particular  elevation  and  the  distance  of 
the  body. 

a.  Other  corrections  would  also  have  to  be  made  to  obtain  the  exact 
altitude  ;  namely,  for  the  dip  of  the  horizon  caused  by  the  elevation  of 
the  spectator,  and  for  the  effect  of  the  atmosphere  upon  the  direction 
of  the  rays  of  light  which  pass  through  it.  The  latter  of  these  is 
called  Refraction. 

REFRACTION. 

89.  REFRACTION,  in  astronomy,  is  the  change  of  direction 
which  the  rays  of  light  undergo  in  passing  through  the 
earth's  atmosphere. 

a.  It  is  a  general  fact  that  the  rays  of  light  when  passing  obliquely, 
from  one  medium  into  another  of  a  different  density,  are  turned  from 
their  course,  and  made  to  pass  more  obliquely,  if  the  medium  which 
they  enter  is  rarer,  and  less  obliquely,  if  it  is  denser  than  that  which 
they  leave.  Thus,  in  passing  from  air  into  water,  or  from  water  into 
glass,  the  direction  would  be  less  oblique  ;  but  in  passing  from  water 
into  air,  more  oblique. 

Suppose  n  m  to  represent  the  surface  of  water,  Fig  42 . 

and  S  0  a  ray  of  light,  entering  the  water  at  O. 
Instead  of  keeping  on  in  the  direction  8  O,  it  is 
bent  toward  the  perpendicular  A  B,  and  thus 
passes  less  obliquely. 


b.  Now,  as  the  earth's  atmosphere  is  not  of 
uniform  density,  but  grows  more  and  more 
dense  toward  the  surface  of  the  earth,  the 
rays  of  light  which  proceed  from  any  body 

are  constantly  bent  more  and  more  toward  a  perpendicular  direction  ; 
and  since  we  see  an  object  in  the  direction  in  which  the  ray  of  light 
strikes  the  eye,  the  apparent  altitude  of  the  body  will  be  increased. 

QUESTIONS.— a.  What  other  corrections  required  for  true  altitude?  89.  What  is 
refraction  ?  «.  State  the  general  law.  Explain  by  the  diagram,  b.  Why  is  the  alti- 
tude increased  by  refraction  ?  Explain  by  the  diagram. 


REFRACTION. 

Suppose  E  to  represent  the 
earth,  and  A  B  C  D,  portions 
or  strata  of  the  atmosphere,  of 
different  densities,  P,  the  place 
of  observation.  Suppose  a  ray 
of  light  from  the  star  S,  strike 
the  atmosphere  at  a;  on  ac- 
count of  refraction,  instead  of 
proceeding  in  the  direction  S 
A,  it  describes  a  &,  b  c,  and  c  P, 
reaching  the  spectator  at  P, 
and  in  the  direction  of  c  P ;  so 
that  the  star  appears  in  that 

/  E  \    \    \     \  direction    at    S',  and  is   thus 

ABCD  ABCD  elevated  above  its  true  posi- 

tion at  S.    As  the  atmosphere 

does  not  consist  of  distinct  strata,  as  represented,  but  diminishes  uniformly 
in  density  from  the  surface  of  the  earth,  the  broken  line  a  b  c  P,  is  in  real- 
ity a  curve,  and  the  line  S'  P,  a  tangent  to  it  at  the  point  P. 

90.  The  effect  of  refraction  is  greatest  upon  a  body  when 
it  is  in  the  horizon,  and  diminishes  toward  the  zenith,  where 
it  is  nothing.     At  the  horizon,  it  amounts  to  about  33 
minutes. 

a.  There  is  no  refraction  at  the  zenith,  because  at  that  point  every 
ray  of  light  strikes  the  atmosphere  perpendicularly,  and  refraction  only 
takes  place  when  the  direction  of  the  rays  is  oblique  ;  at  the  horizon, 
they  are  more  oblique  than  they  can  be  at  any  point  above  it ;  hence 
the  refraction  is  greatest  there. 

91.  At  the  horizon,  the  amount  of  refraction  is  somewhai 
greater  than  the  apparent  diameter  of  the  sun  or  moon ;  and 
hence  these  bodies  appear  to  be  above  the  horizon  when 
they  are  actually  below  it. 

a.  The  times  of  the  rising  of  all  the  heavenly  bodies  are,  therefore, 
accelerated,  and  those  of  their  setting  retarded,  by  refraction  ;  each 
one  appears  to  be  above  the  horizon  before  it  has  actually  risen,  and 
is  seen  above  the  horizon  after  it  has  actually  set. 


.— 90.  What  is  the  effect  of  refraction  at  the  zenith  and  horizon  ?  Why  ? 
91.  What  is  the  amount  of  refraction  at  the  horizon?  a.  Effect  on  the  rising  and  set- 
ting of  the  heavenly  hodies  ? 


APPARENT     MOTIONS     OF    THE     SUN.  63 

6.  Refraction  very  rapidly  diminishes  from  the  horizon  towards  the 
zenith.  At  the  horizon  its  mean  value  is  33' ;  at  10°  of  altitude,  15 i' ; 
at  30°,  li' ;  at  45°,  57"  ;  at  80°,  10"  ;  at  90°,  0. 


SECTION    III. 

APPARENT  MOTIONS  OF  THE  SUN  AND  STARS. 

92.  The  sun  has  two  apparent  motions  around  the  earth ; 
namely,  a  diurnal  motion  from  east  to  west,  and  an  annual 
motion  from  west  to  east.  The  first  is  caused  by  the  rota- 
tion of  the  earth  on  its  axis,  and  the  second,  by  its  revolu- 
tion around  the  sun. 

(l.  The  student  should  be  careful  to  verify  by  his  own  observations 
the  following  statements  respecting  the  sun's  apparent  motions  : — 

1.  Apparent  Daily  Motion.— The  sun  rises  exactly  at  the  east  point 
of  the  horizon,  and  sets  at  the  west  point,  twice  a  year ;  namely,  about 
the  20th  of  March  and  23d  of  September  ;  and,  on  these  days,  it  crosses 
the  meridian  at  an  altitude  equal  to  the  complement  of  the  latitude  ; 
that  is,  at  the  point  where  the  celestial  equator  crosses  the  meridian. 

2.  From  March  20th  to  June  21st,  the  points  at  which  the  sun  rises 
and  sets  move  from  the  east  and  west  toward  the  north,  and  its  merid- 
ian altitude  constantly  increases  ;  from  June  21st  till  Sept.  23rd,  the 
points  of  rising  and  setting  move  back  toward  the  east  and  west,  and 
the  meridian  altitude  diminishes ;  from  Sept.  23rd  to  Dec.  22nd,  the 
points  of  rising  and  setting  move  toward  the  south,  and  the  meridian 
altitude  diminishes  ;  from  Dec.  22nd  to  March  20th,  the  points  of  rising 
and  setting  move  back  toward  the  east  and  west,  and  the  meridian  alti- 
tude increases.    There  is  thus  a  constant  movement  of  the  points  of 
rising  and  setting  alternately  from  north  to  south,  and  a  constant 
variation,  up  and  down,  of  the  point  of  culmination,  except  that  the 
sun  culminates  at  the  same  altitude  for  several  days,  about  the  21st  of 

QUESTIONS. — b.  How  fast  does  refraction  diminish  from  the  horizon?  92.  What  ap- 
parent motions  has  the  sun  ?  How  caused  ?  a.  State  the  daily  phenomena  connected 
with  the  apparent  motions  of  the  sun.  What  changes  in  the  points  of  rising  and  set- 
ting ?  In  the  point  of  culmination  ?  Solstices  and  equinoxes  ? 


64  APPARENT    MOTIONS     OF 

June  and  the  22nd  of  December.  These  two  stationary  points  of  cul- 
mination are  called  the  Solstices.*  The  points  ut  which  the  culmina- 
tion of  the  sun  coincides  with  that  of  the  celestial  equator  are  called 
the  Equinoxes,\  because  when  the  sun  is  at  either  of  these  points,  the 
days  and  nights  are  exactly  equal  to  each  other. 

3.  Apparent  Annual  Motion. — The  sun  appears  to  move  toward 
the  east  among  the  stars  ;  for,  if  on  any  evening  at  sunset,  or  a  short 
time  after,  we  notice  the  distance  of  the  sun  from  any  star  that  may  be 
visible,  we  shall  find,  in  a  few  evenings,  that  this  distance  has  grown 
less  ;  and  hence,  as  the  stars  are  fixed  points,  that  the  sun  has  moved 
toward  the  east.  This  motion  will  continue  from  month  to  month 
until  the  sun  will  be  in  conjunction  with  the  star;  and  then  for  six 
months  the  star  will  be  no  longer  visible,  but  at  the  end  of  that  time, 
will  show  itself  above  the  eastern  edge  of  the  horizon  just  as  the  sun 
sets  below  the  western  ;  and  at  the  expiration  of  one  year  from  the 
first  observation,  will  have  returned  to  the  same  relative  position  with 
the  sun.  In  this  way  the  sun  appears  to  move  from  star  to  star  toward 
the  east,  completing  its  circuit  in  365  J-  days. 

93.  The  great  circle  of  the  celestial  sphere  in  which  the 
sun  appears  to  revolve  around  the  earth  every  year,  is  called 
the  ECLIPTIC. 

The  ecliptic  may  also  be  defined  as  the  great  circle  of  the  celestial 
sphere  in  which  it  is  intersected  by  the  plane  of  the  earth's  orbit.  Hence 
the  plane  of  the  ecliptic  is  the  plane  of  the  earth's  orbit. 

94.  The  great  circle  of  the  celestial  sphere  exactly  over 
the  equator    is  called  the    EQUINOCTIAL,    or    CELESTIAL 
EQUATOR. 

The  student  must  conceive  these  circles  as  marked  out  on  the  sky, 
the  one  crossing  the  other.  (See  diagram,  Fig.  44.) 

95.  Since  the  earth's  axis  is  inclined  to  the  plane  of  its 


*From  the  Latin  words  sol,  meaning  the  sun,  and  sto,  meaning  to  stand. 
t  From  the  Latin  words  equus,  meaning  equal,  and  nox,  meaning  night.    The 
arrival  of  the  sun  at  either  of  these  points  produces  equal  days  and  nights. 

QUESTIONS.— State  the  phenomena  connected  with  the  snn's  apparent  annual  motion. 
03.  What  is  the  ecliptic  ?  94.  What  is  the  equinoctial  ?  95.  What  is  meant  by  the 
obliquity  of  the  ecliptic  ?  Why  is  it  23 J  °  ? 


THE    SUN    AND    STAES.  65 

orbit,  or  the  plane  of  the  ecliptic,  making  with  it  an  angle 
of  66A°,  the  ecliptic  and  equinoctial  must  cross  each  other 
at  an  angle  of  23  ,J°.  This  angle  is  called  the  OBLIQUITY  OF 
THE  ECLIPTIC. 

Fig.  44. 
pOLE_OF_£CUpr/c 


P°LE  OF   ECLIPTIC 

ECLIPTIC  AND   EQUINOCTIAL. 

a.  The  obliquity  of  the  ecliptic,  and,  of  course,  the  inclination  of  the 
axis,  are  indicated  by  the  difference  between  the  highest  and  lowest 
daily  culminating  points  of  the  sun,  being  equal  to  one-half  of  this  dif 
ference.  For  when  it  is  at  the  equinoctial,  it  must  culminate  where 
the  equinoctial  crosses  the  meridian,  that  is,  at  an  altitude  equal  to  the 
complement  of  the  latitude  ;  and  when  it  is  north  or  south  of  the  equi- 

i.  How  is  the  obliquity  of  the  ecliptic  indicated? 


66 


APPARENT    MOTIONS     OF 


noctial,  it  must  culminate  as  far  above  or  below  the  culminating  point 
of  the  equinoctial.  But  this  never  exceeds  23  i°  either  way ;  hence, 
the  obliquity  or  inclination  must  be  23  £°.  This  departure  of  the  sun 
from  the  equinoctial,  as  indicated  by  its  daily  motion,  is  called  its 
Declination. 

b.  To  find  the  greatest  and  least  meridian  altitude  of  the  sun  at  any 
place,  the  following  rule  may  be  given  :  Find  the  complement  of  the 
latitude,  and  to  it  add  23£°  for  the  greatest  altitude  ;  and  from  it  sub- 
tract 23i°  for  the  least.     Thus  for 
Fig.  45.  New  york  the  lat    of  which  is 

about  40,L° :  90°  -  40F  =  49£° 
comp.  of  lat.  Hence,  49^°  +  23^° 
=  73°,  greatest  altitude ;  and  49^° 
—  23jr°  =  26°,  least  altitude. 

In  the  diagram,  P  P  represents 
the  celestial  poles,  E  E  the  equi- 
H  noctial,  Z  N  the  zenith  and  nadir, 
H  H  the  horizon,  8  the  position  of 
the  sun  when  23|°  north  of  the 
equinoctial,  and  S'  its  position 
when  23i°  south  of  the  equinoctial ; 
then  E  H  will  represent  its  alti- 
tude when  at  the  equinoctial,  E  H 
+  E  S,  its  greatest  meridian  alti- 
;  and  E  H  —  E  S',  its 


G3EATE8T  ANI>  LEAST  ALTITUDE   OF   THE   SUN. 


96.  The  two    opposite  points  of  the  ecliptic,   where  it 
crosses  the  equinoctial,  are  called  .the  EQUINOCTIAL  POINTS, 
or  EQUINOXES.    The  one  which  the  sun  passes  in  March  is 
called  the  Vernal  Equinox  ;  that  which  it  passes  in  Septem- 
ber, the  Autumnal  Equinox. 

97.  The  two  opposite  points  of  the  ecliptic  at  which  the 
sun  is  farthest  from  +he  equinoctial,  are  called  the  SOLSTITIAL 
POINTS,  or  SOLSTICES.     The  one  north  of  the  equinoctial  is 
called  the  Summer  Solstice  ;  the  one  south  of  it,  the  Winter 
Solstice. 

QUESTIONS —ft.  How  to  find  the  greatest  and  least  meridian  altitude  of  the  sun? 
Explain  by  the  diagram.  06.  What  are  the  equinoxes?  How  distinguished?  97.  The 
solstices,  and  how  distinguished  ? 


THE    SUN    AND    STABS.  67 

a.  The  equinoxes  and  solstices  are  sometimes  called  the  cardinal 
points  of  the  ecliptic ;  they  are  90°  from  each  other,  and,  of  course, 
divide  the  ecliptic  into  four  equal  parts. 

98.  The  DECLINATION  of  a  heavenly  body  is  its  distance, 
north  or  south,  from  the  equinoctial. 

a.  Declination  corresponds  to  terrestrial  latitude.    At  the  equinoxes, 
the  decimation  of  the  sun  is  0°  ;  at  the  solstices,  it  is  23£°,  which  is  the 
greatest  declination  the  sun  can  have. 

b.  In  a  right  sphere,  the  amplitude  of  the  sun  when  it  is  rising  or 
setting,  is  exactly  equal  to  its  declination.     [Let  the  student  verity  this 
by  an  artificial  globe.] 

99.  CIRCLES  OF  DECLINATION   are  great  circles  of  the 
celestial  sphere  that  pass  through  the  poles,  and  are  perpen- 
dicular to  the  equinoctial. 

a.  Hour  Circles. — Circles  of  declination  correspond  to  meridian 
circles  on  the  earth.     When  drawn  at  intervals  of  15°,  they  are  called 
Hour  Circles,  because  the  heavenly  bodies,  in  their  apparent  diurnal 
revolution  round  the  earth,  pass  from  one  to  the  other  every  hour ; 
since  360°  +  24  =  15°. 

b.  Hour  Angle. — The  angle  included  between  the  hour  circle  pass- 
ing through  a  body  and  the  meridian  of  the  place  of  observation  is 
called  the  Hour  Angle  of  the  body. 

c.  Colures. — The  circle  of  declination  that  passes  through  the  equi- 
noctial points  is  called  the  Equinoctial  Colure;  that  which  passes 
through  the  solstitial  points  is  called  the  Solstitial  Colure. 

<l.  The  position  of  a  heavenly  body  in  the  celestial  sphere  is  defined 
by  its  distance  from  the  equinoctial  (or  declination),  and  its  distance 
from  the  equinoctial  colure,  reckoned  eastward  from  0°  to  360°.  The 
latter  is  called  its  Right  Ascension. 

100.  The  RIGHT  ASCENSION  of  a  heavenly  body  is  its 
distance  from  the  equinoctial  colure,  reckoned  on  the  equi- 

QUFSTIONS.— «.  What  are  these  points  sometimes  called?  98.  What  is  declination  ? 
a.  Greatest,  declination  of  the  sun  ?  b.  Amplitude  of  the  sun  in  a  right  sphere— equal 
to  what?  99.  What  are  circles  of  declination?  n.  What  are  hour  circles?  ft.  What 
is  the  hour  anj?le?  r.  What  are  eolures?  d.  How  is  the  position  of  a  body  in  the 
celestial  sphere  defined  1  100.  What  is  right  ascension  ? 


68 


SIGNS    OF    THE    ECLIPTIC. 


noctial  from  the  vernal  equinox  eastward  entirely  around 
the  circle,  that  is,  from  0°  to  360°. 

a.  Right  ascension  is  frequently  expressed  in  hours,  minutes,  and 
seconds  ;  reckoning,  of  course,  15°  to  an  hour.  (See  Art.  71,  b.)  Thus, 
150°  30'15"  =  10h  2ra  1'. 


SIGNS  OF  THE  ECLIPTIC. 

101.  The  ecliptic  is  divided  into  twelve  equal  parts,  called 
SIGNS.    Each  sign,  therefore  contains  30  degrees. 

102.  The  following  are  the  names  of  the  signs,  the  char- 
acters denoting  them,  and  the  day  of  the  month  on  which 
the  sun  enters  each  (1867) : 


(  ARIES 
< TAURUS 
'  GEMINI 


Spring 
Signs. 


Summer  ( 

Signs'    (VIRGO 

Autumn  (  LlBRA 
Signs.    )  ScORPI° 

(  SAGITTARIUS 

Winter  (  CAPRICORNUS 
Signs,    j  DARIUS 
(  PISCES 


n 

25 


I 

V? 


March  20. 
April  20. 
May  21. 
June  21. 
July  23. 
August  23. 
September  23. 
October  23. 
November  23. 
December  22. 
January  20. 
February  18. 


VERNAL  EQUINOX. 


SUMMER  SOLSTICE. 


AUTUMNAL  EQUINOX 


WINTER  SOLSTICE. 


a.  The  equinoctial  points  are,  it  will  be  observed,  at  the  first  degree 
of  Aries  and  Libra  ;  and  the  solstitial  points  at  the  first  degree  of  Can- 
cer and  Capricorn. 

103.  The  ZODIAC  is  a  zone  of  the  celestial  sphere,  extend- 
ing to  the  distance  of  eight  degrees  on  each  side  of  the 
ecliptic. 

a.  The  zodiac  is  therefore  16°  wide ;  and  within  its  limits  are  con- 

QUESTIONS.— a.  How  is  right  ascension  frequently  expressed  ?  101.  How  is  the  eclip- 
tic divided?  102.  Name  the  signs,  and  the  day  on  which  the  sun  enters  each.  a.  At 
which  of  the  signs  are  the  equinoxes  and  solstices  t  Date  of  each  ?  103.  What  is  the 
zodiac  ?  a.  What  is  its  width  ?  What  does  it  contain  ? 


PKECESSIOK.  69 

tained  the  orbits  of  all  the  planets,  except  some  of  the  Minor  Planets. 
It  also  contains  twelve  of  the  great  groups  of  stars,  called  the  Constel- 
lations of  the  Zodiac,  which  have  the  same  names,  and  occupy  nearly 
the  same  places,  as  the  signs  of  the  ecliptic.  The  names  given  to  the 
signs  are  properly  the  names  of  the  constellations :  Aries,  tJie  ram  ; 
Taurus,  the  bull;  Gemini,  the  twins;  Cancer,  the  crab;  Leo,  the  lion; 
Virgo,  the  virgin;  Libra,  the  balance;  Scorpio,  the  scorpion;  Sagit- 
tarius, the  archer  ;  Capricornus,  the  goat ;  Aquarius,  the  water-carrier  ; 
Pisces,  the  fishes. 

b.  The  places  of  the  signs  nearly  corresponded  with  those  of  the 
constellations  in  the  time  of  Hipparchus,  by  whom  the  constellations 
of  the  sphere  were  classified  and  arranged.  He  was  the  first  to  dis- 
cover (125  B.  C.)  the  displacement  of  the  signs,  and  to  explain  its 
cause, — the  falling  back  (from  east  to  west)  of  the  equinoxes.  This 
movement  of  the  equinoctial  points  is  called  precession. 

PRECESSION. 

104.  PRECESSION  is  a  gradual  falling  back  of  the  equinoc- 
tial points  from  east  to  west. 

In  other  words,  the  sun,  in  his  apparent  annual  revolution  around 
the  earth,  does  not  cross  the  equinoctial  always  at  the  same  points, 
but  at  every  revolution  crosses  a  little  to  the  west  of  the  points  at 
which  it  crossed  previously.  The  irregularity  seems  to  exist  in  the 
motion  of  the  sun ;  but,  of  course,  it  is  really  in  the  motion  of  the 
earth. 

105.  The   amount  of   precession  annually  is  about  50 
seconds  (50.2") ;  and  consequently,  to  pass  quite  round  the 
circle,  the  equinoxes  require  a  period  of  nearly  26,000  years. 

a.  For  360°  X  60  X  60  =  1,296,000"  •*  50.2"  =  25,816. 

b.  In  the  time  of  Hipparchus,  the  vernal  equinox  was  in  the  con- 
stellation  Aries  ;  but  it  is  now  in  Pisces,  having  fallen  back  about  28°. 
The  signs  and  constellations  corresponded  about  185  B.  C. 

QUESTIONS.— ft.  When  did  the  signs  of  the  ecliptic  and  the  constellations  of  the  zodiac 
correspond  ?  104.  What  is  precession  ?  Explain  it.  105.  What  is  the  amount  annu- 
ally ?  a.  Period  required  for  a  revolution  ?  ft.  In  what  constellation  is  the  vernal  equi- 
aox  ?  Where  was  it  in  the  time  of  Hipparchus  ? 


70  THE    TERRESTRIAL    GLOBE. 

c.  In  maps  of  the  heavens,  and  catalogues  of  the  stars,  the  places  of 
stars  are  marked  by  their  declinations  and  right  ascensions  ;  in  some, 
however,  they  are  indicated  by  their  latitudes  and  longitudes,  which 
terms,  when  applied  to  celestial  objects,  have  a  different  meaning  from 
that  which  they  have  as  applied  to  places  on  the  earth's  surface. 

CELESTIAL  LATITUDE  AND  LONGITUDE. 

106.  The  LATITUDE  OF  A  HEATEDLY  BODY  is  its  distance 
from  the  ecliptic,  north  or  south. 

Celestial  latitude  must  of  course  be  reckoned  upon  a  secondary  to 
the  ecliptic,  from  0°  to  90°. 

107.  The  LONGITUDE  OF  A  HEAVENLY  BODY  is  its  dis- 
tance from  a  secondary  to  the  ecliptic  which  passes  through 
the  vernal  equinox,  or  first  degree  of  Aries.    It  is  reckoned 
from  the  vernal  equinox  eastward  from  0°  to  360°. 

a.  Of  course,  neither  the  longitude  nor  right  ascension  of  a  body 
can  be  quite  equal  to  360°  ;  since  that  would  bring  it  back  to  the  point 
of  commencement,  or  0° ;  it  may,  however,  be  any  distance  less  than 
that;  as,  359°  59' 59". 

PROBLEMS  FOR  THE  TERRESTRIAL  GLOBE. 

PROBLEM  I. — To  find  the  sun's  longitude  for  any  given 
day :  Look  for  the  given  day  of  the  month  on  the  wooden 
horizon,  and  the  sign  and  degree  corresponding  to  it,  in  the 
circle  of  signs,  will  be  the  sun's  place  in  the  ecliptic ;  find 
this  place  on  the  ecliptic,  and  the  number  of  degrees  between 
it  and  the  first  point  of  Aries,  counting  toward  the  east, 
will  be  the  sun's  longitude. 

EXAMPLES. 

1.  What  is  the  longitude  of  the  sun  June  21st  ?    Ans.  90°. 

2.  (What  is  it  February  22d  ?  Ans.  334^°. 

3.  'What  is  it  May  10th  ?  Ans.  50°. 

QUESTIONS.— c.  Places  of  stars— how  marked  on  maps  ?  lOd.  What  is  celestial  latiU 
trade?  How  reckoned?  107.  What  is  celestial  longitude?  ^ow  reckoned?  a.  Can 
the  longitude  be  360°  ? 


THE    TEEKESTKIAL    GLOBE.  71 

PROBLEM II. — To  find  the  right  ascension  of  the  sun: 
Bring  the  sun's  place  in  the  ecliptic  to  the  edge  of  the  brass 
meridian ;  and  the  degree  of  the  equinoctial  over  it,  reck- 
oning from  the  first  degree  of  Aries,  toward  the  east,  will  be 
the  right  ascension. 

EXAMPLES. 

1.  What  is  the  right  ascension  of  the  sun  October  18th  ?    Ans.  203£°. 

2.  What  is  it  May  2d  ?  Ans.  42°. 

PROBLEM  III. — To  find  the  declination  of  the  sun:  Bring 
the  sun's  place  in  the  ecliptic  to  the  edge  of  the  brass  merid- 
ian; and  the  degree  of  the  meridian  over  it,  reckoning 
from  the  equator,  will  be  the  declination.  The  declination 
may  also  be  found  by  bringing  the  given  day  of  the  month 
as  marked  on  the  analemma  to  the  meridian. 

EXAMPLES. 

1.  What  is  the  declination  of  the  sun  June  21st  ?    Ans.  23£°  N. 

2.  What  is  its  declination  Jan.  27th  ?  Ans.  18i°  S. 

3.  What  is  it  April  16th  ?  Ans.  10°  N. 

PROBLEM  IV. — To  find  what  places  have  a  vertical  sun  on 
any  day  in  the  year :  Find  the  sun's  declination,  and  note  the 
degree  on  the  brass  meridian ;  then  turn  the  globe  around, 
and  all  places  that  pass  under  that  degree  will  be  those 
required. 

EXAMPLES 

1.  What   places  have  a  vertical  sun  March  20th  ?    Ans.  All  places 

under  the  Equator. 

2.  To  what  places  is  the  sun  vertical  December  22d?     Ans.  To  all 

places  under  the  Tropic  of  Capricorn. 

3.  To  what  places  is  the  sun  vertical  May  1st  ?     Ans.  To  all  in  lati- 

tude 16°  N. 

PROBLEM  V. — To  find  the  meridian  altitude  of  the  sun 
for  any  day  of  the  year,  at  any  place :  Make  the  elevation  of 
the  north  or  south  pole  above  the  wooden  horizon  equal  to 


72  THE     TERRESTRIAL     GLOBE. 

the  latitude,  so  that  the  wooden  horizon  may  represent  the 
horizon  of  that  place ;  bring  the  sun's  place  in  the  ecliptic 
to  the  brass  meridian,  and  the  number  of  degrees  on  the 
meridian  from  the  horizon  to  the  sun's  place  will  be  the 
meridian  altitude. 

EXAMPLES. 

1.  Find  the  sun's  meridian  altitude  at  New  York,  June  21st.  Ans.  73°. 

2.  At  London,  Jan.  27th.  Ans.  20°. 

3.  Rio  de  Janeiro,  September  23d.  Ans.  67°. 

PROBLEM  VI. — To  find  the  amplitude  of  the  sun  at  any 
place,  and  for  any  day  in  the  year :  Proceed  as  in  Problem  V. ; 
then  bring  the  sun's  place  to  the  eastern  or  western  edge  of 
the  horizon,  and  the  number  of  degrees  on  the  horizon  from 
the  east  or  west  point  will  be  the  amplitude. 

EXAMPLES. 

1.  Find  the  sun's  amplitude  at  London,  June  21st.     Ans.  39|°  N. 

2.  At  Quito,  September  23d.  Ans.     0°. 

3.  At  Philadelphia,  July  16th.  Ans.  28°  N. 

PROBLEM  VII. — To  find  the  suns  altitude  and  azimuth  at 
any  place,  for  any  day  in  the  year,  and  any  hour  of  the  day  : 
Proceed  as  in  Problem  V. ;  then  set  the  index  to  twelve,  and 
turn  the  globe  eastward  or  westward,  according  as  the  time 
is  before  or  after  noon,  until  the  index  points  to  the  given  hour. 
Then,  for  a  vertical,  screw  the  quadrant  of  altitude  over  the 
zenith,  and  bring  its  graduated  edge  to  the  sun's  place  in  the 
ecliptic ;  the  number  of  degrees  on  the  quadrant  from  the 
sun's  place  to  the  horizon  will  be  the  altitude,  and  the  num- 
ber of  degrees  on  the  horizon,  from  the  meridian  to  the 
edge  of  the  quadrant,  will  be  the  azimuth. 

E  XAMPLES. 

1.  Find  the  sun's  altitude  and  azimuth  at  New  York,  May  10th,  9 
o'clock  A.  M.     Ans.  Altitude,  45^°  ;  azimuth,  72^°  E. 


DAY    AND     NIGHT. 


73 


2.  At  London,  May  1st,  10  o'clock  A.  M.    Ans.  Altitude,  47°;   azi- 

muth, 44°  E. 

3.  At  London,  March  20th,  3i  o'clock  P.  M.    Ana.  Altitude  22° ;   azi- 

muth, 59°  W. 


SECTION    IV. 

DAY  AND   NIGHT. 

108.  The  succession  of  day  and  night  is  caused  by  the 
rotation  of  the  earth  on  its  axis. 

As  the  earth  turns  on  its  axis,  every  place  is  brought  alternately 
into  the  light  and  into  the  shade.  All  places  turned  toward  the  sun, 
so  that  its  rays  can  shine  upon  them,  have  day ;  and  those  turned 
away  have  night,  because  they  are  in  the  earth's  shadow. 

109.  The  comparative  length  of  day  and  night  at  any  par- 
ticular place  and  time  depends  upon  the  sun's  declination, 
or  distance  from  the  equinoctial.    When  the  sun  is  north  of 
the  equinoctial,  all  places  in  the  northern  hemisphere  have 
longer  day  than  night,  and  those  in  the  southern  hemisphere, 
longer  night  than  day ;  but  when  the  sun  is  south  of  the 


equinoctial,  this  is  reversed. 

In  the  diagram,  let  H  H  represent  the 
horizon,  P  P'  the  axis  of  the  celestial 
sphere,  E  W  the  equinoctial ;  let  also  8 
be  the  sun  in  north  declination,  and  8' 
in  south  declination  ;  it  will  be  obvious 
that  as  the  earth  turns,  the  sun  at  S  will  H 
appear  to  move  in  a  diurnal  arc,  as  a  8  J, 
greater  than  the  nocturnal  arc  a  c  b  ;  and 
at  8',  the  diurnal  arc  m  8'  n  will  be  less 
than  the  nocturnal  arc  mon;  while  at  E, 
in  the  equinox,  the  circle  of  daily  motion 
described  by  the  sun  will  be  divided 
equally  by  the  horizon. 


Pig.  46. 


LONGEST  DAY   AND   NIGHT. 


QUESTIONS.— 108.  What  causes  the  succession  of  day  and  night  ?  109.  On  what  doea 
the  length  of  day  and  night  depend  ?  How  does  the  day  compare  with  the  night  when 
the  sun  is  north  of  the  equinoctial  ?  When  south  of  it  ?  Explain  by  the  diagram. 


74  DAY    AND    NIGHT. 

110.  All  places  under  the  equator  have  equal  days  and 
nights  during  the  whole  year. 

a.  This  will  be  obvious,  if  it  is  remembered  that  in  a  right  sphere, 
all  the  circles  of  daily  motion  are  perpendicular  to  the  horizon,  and 
equally  divided  by  it  ;  so  that  whatever  the  declination  of  the  sun 
may  be,  its  diurnal  arc  must  always  be  equal  to  its  nocturnal  arc. 

ft.  One  half  of  the  year,  to  places  under  the  equator,  the  sun  is  in 
the  north  when  on  the  meridian,  and  the  other  half  in  the  south  ; 
while  on  the  20th  of  March  and  the  23d  of  September,  it  is  exactly 
overhead,  or  vertical 

c.  Since  the  sun's  declination  is  never  greater  than  23£°,  no  place 
whose  latitude,  either  north  or  south,  is  beyond  that  limit,  can  have  a 
vertical  sun  ;  and  all  places  within  these  limits  must  have  a  vertical 
sun  twice  every  year  ;  that  is,  as  the  sun  moves  north  and  on  its  return. 

111.  The  small  circles  parallel  to  the  equator  or  equinoc- 
tial, at  the  limit  of  the  sun's  declination,  are  called  the 
Tropics  ;  that  at  the  northern  solstice  is  called  the  TROPIC 
OF  CANCER  ;  that  at  the  southern,  the  TROPIC  OF  CAPRI- 
CORN. 

a.  Tropic  means  turning  ;  and  these  circles  are  called  tropics,  because, 
when  the  sun  arrives  at  one,  it  turns  back  and  goes  to  the  other.  They 
serve  to  bound  that  zone  of  the  earth's  surface  within  which  the  sun 
can  be  vertical. 


Places  situated  at  either  of  the  poles  have  constant 
day  during  the  whole  six  months  the  sun  is  in  the  same 
hemisphere  ;  and  constant  night  during  the  six  months  it  is 
in  the  other. 

a.  For  in  a  parallel  sphere,  the  equinoctial  coincides  with  the  hori- 
zon, and  therefore,  when  the  sun  is  north  of  the  equinoctial,  it  must 
be  above  the  horizon,  and  when  south  of  the  equinoctial,  below  it. 

b.  Since  the  altitude  of  the  pole  is  equal  to  the  latitude,  (Art,  82,  a.) 


QUESTIONS. — 110.  Day  and  night  at  places  under  the  equator?  «.  Why?  ft.  When 
is  the  sun  vertical?  c.  What  places  can  have  a  vertical  sun?  111.  What  are  the 
tropics?  How  named  ?  a.  What  does  tropic  mean  ?  112.  What  places  have  constant 
day,  and  when?  a.  Why?  6.  How  often  does  the  sun  cross  the  meridian  at  these 
places  ?  Explain  by  the  diagram  (Fig.  47). 


DAT     AND     NIGHT. 


75 


the  distance  of  the  circle  of  perpetual  apparition  from  the  equator 
is  equal  to  the  complement  of  the  latitude  ;  and  when  the  sun  is 
within  this  circle,  there  must  be  constant  day  ;  the  sun  keeping  above 
the  horizon,  and  crossing  the  meridian  twice  during  the  twenty-four 
hours, — once  when  it  culminates,  in  the  south  or  north,  according  as 
the  place  is  in  north  or  south  latitude,  and  once  at  the  opposite  part  of 
the  circle. 

Suppose  Z  to  be  the  zenith 
of  a  place  15°  from  the  north 
pole,  and  consequently  in  75° 
N.  latitude;  H  H'  being  the 
plane  of  the  horizon,  P  P  the 
celestial  poles,  E  E  the  plane 
of  the  equinoctial,  S  the  sum- 
mer solstice,  and  W  the 
winter  solstice  :  then  P  H'  = 
75°,  and  a  W  is  the  circle  of 
perpetual  apparition,  and  H  & 
the  circle  of  perpetual  occul- 
tation.  At  d  the  sun  has  15° 
of  north  declination,  and  at 
its  point  of  culmination,  a, 
crosses  the  meridian  at  an  al- 
titude of  30°  (H  E  +  E  a); 
while  at  the  opposite  point  it 
just  touches  the  horizon  at  H'; 
H'  is  obviously  the  north,  because  it  is  toward  the  pole.  Going  north  from  d 
toward  the  solstice  S,  and  back  from  S  to  c,  it  is  evident  that  the  sun  will  be 
within  the  circle  of  perpetual  apparition,  and  hence,  there  will  be  constant 
day ;  while  from  c  to  e,  the  equinox,  and  from  e  to  w,  the  circle  of  perpetual 
occultation,  it  will  rise  and  set,  its  meridian  altitude  growing  less  and  less 
until  at  n,  it  will  appear  at  the  horizon  for  a  short  time  at  noon  each  day, 
and  finally  disappear,  remaining  below  the  horizon  while  <roing  south  from 
n  to  W,  the  winter  solstice,  and  north  from  W  to  m,  where  it  again  crosses 
the  circle  of  perpetual  occultation,  and  then  appears  once  more  above  the 
horizon.  There  is,  therefore,  constant  day  while  it  is  passing  over  d  Sc,  and 
constant  night  while  passing  over  n  W  m. 

c.  Since  the  smallest  circle  of  perpetual  apparition  or  of  perpetual 
occultation  reached  by  the  sun  extends  66  V°  from  the  pole,  no  place 
situated  within  66^°  from  the  equator,  can  have  constant  day,  or  day 


CONSTANT   DAT    AND   NIGHT. 


QUESTIONS.— c.  What  is  the  limit  of  constant  day  and  night  ? 


76 


DAY    AND    JSTIGHT. 


S.Pole 

POLAB  CIBCLE8. 


of  more  than  24  hours'  duration.  Hence,  the  limit  of  constant  day  is 
the  small  circle  round  each  pole,  23£°  Irom  it.  These  two  parallels 
are  called  polar  circles. 

113.  The  POLAB  CIRCLES  are  two 
small  circles,  parallel  to  the  equa- 
tor or  equinoctial,  and  231°  from 
the  poles.   The  one  round  the  north 
pole  is  called  the  ARCTIC  CIRCLE  ; 
the  one  round  the  south  pole,  the 
ANTARCTIC  CIRCLE. 

114.  All  places  within  the  polar 
circles  have  constant  day  and  con- 
stant night  during  a  portion  of 
each  year;   the  duration  of  each 

being  greater  or  less  according  as  the  place  is  nearer  to  the 
pole  or  farther  from  it. 

The  polar  circles  serve  to  mark  the  limit  of  constant  day  and  night. 

PiK<  4a  115.  When  the  sun  is  in 

either  of  the  solstices,  all 
places  in  the  same  hemi- 
sphere with  it  have  their 
longest  day  and  shortest 
night,  and  those  in  the 
other,  their  shortest  day  and 
longest  night.  When  it  is 
in  either  of  the  equinoxes, 
the  days  and  nights  are  of 

equal  length  in  all  parts  of  the  earth,  except  at,  or  very  near, 

the  poles. 

116.  The  atmosphere  of  the  earth  increases  the  length 

of  the  day,  both.by  refracting  and  by  reflecting  the  sun's  rays. 

QUESTIONS  —113.  What  are  the  polar  circles  ?  How  named  ?  114.  What  places  hare 
constant  day  or  night?  115.  What  is  said  of  the  day  and  night  when  the  sun  enters 
either  solstice  ?  Either  equinox  ?  116.  How  is  the  length  of  the  day  increased  ? 


EARTH   AT  THE   SOLSTICE. 


TWILIGHT. 


77 


EARTH   AT   THE   EQUINOX. 


a.  When  the  sun  is  in  either  Fig-  5O* 

of  the  equinoxes,  one  half  of  it 
would  constantly  appear  above  the 
horizon  of  a  place  at  either  of  the 
poles,  except  for  refraction,  the 
effect  of  which  is  very  great  at 
those  points  ;  so  that  the  sun,  at 
the  equinox,  appears  wholl7  above 
the  horizon,  thus  causing  constant 
day,  within  one  or  two  degrees  of 
each  pole.  The  general  effect  of 
refraction  is  to  increase  the  length  of  the  day  from  six  to  ten  minutes. 

TWILIGHT. 

117.  When  the  sun  is  a  short  distance  below  the  horizon, 
its  ra}rs  fall  on  the  upper  portions  of  the  atmosphere,  which 
like  a  mirror  reflect  them  upon  the  earth,  and  thus  produce 
that  faint  light  called  twilight.  The  morning  twilight  is 
generally  called  the  dawn. 

Fig.  61. 
H' 


Let  ABC  represent  three  places  on  the  earth,  and  A  H",  B  H',  C  H,  their 
horizons  respectively.  Suppose  8  to  represent  the  sun,  a  little  below  the 
horizon,  its  rays  passing  through  the  atmosphere  in  S  C  H" ;  at  A,  no  por- 
tion of  the  visible  atmosphere  is  illuminated,  and  consequently  there  is  no 
twilight;  at  B,  the  part  H" g  H  is  illuminated,  and  at  C,  H"CH  ;  twilight 
is  produced  at  each  of  these  points. 

"  When  the  sun  is  above  the  horizon,  it  illuminates  the  atmosphere 
and  clouds,  and  these  again  disperse  and  scatter  a  portion  of  its  light 


QTTEBTIONS.— a.  Effect  of  refraction  ?     117.  What  is  twilight,  and  how  produced? 
Explain  by  the  diagram.    Remark  of  Sir  John  Herschel. 


78  TWILIGHT. 

in  all  directions,  so  as  to  send  some  of  its  rays  to  every  exposed  point 
from  every  point  of  the  sky.  The  generally  diffused  light,  therefore, 
which  we  enjoy  in  the  day-time,  is  a  phenomenon  originating  in  the 
very  same  causes  as  twilight.  Were  it  not  for  the  reflective  and  scat- 
tering power  of  the  atmosphere,  no  object  would  be  visible  to  us  out 
of  direct  sunshine ;  every  shadow  of  a  passing  cloud  would  be  pitchy 
darkness ;  the  stars  would  be  visible  all  day,  and  every  apartment  into 
which  the  sun  had  not  direct  admission  would  be  involved  in  noc- 
turnal obscurity." — Sir  John  Herschcl. 

118.  The  duration  of  twilight  varies  greatly  at  different 
parts  of  the  earth ;    it  is   shortest  at    the  equator,  and 
increases  toward  the  poles  ;  near  the  polar  circles  and  within 
them,  there  is  constant  twilight  during  a  part  of  each  year. 

a.  At  the  equator,  the  duration  is  Ih.  12m. ;  at  the  poles,  there  are 
two  twilights  during  the  year,  each  lasting  about  50  days.  This  long 
twilight  diminishes  very  much  the  time  of  total  darkness  at  the  poles ; 
for  the  sun  is  below  the  horizon  six  months,  equal  to  180  days,  and 
deducting  100  days  of  twilight,  there  remain  only  80  days,  or  less  than 
three  months,  of  actual  night. 

119.  Twilight  does  not  cease  until  the  sun  is  about  18° 
below  the  horizon. 

a.  This  is  the  generally  received  estimate,  but  there  is  considerable 
uncertainty  about  it.     Some  have  found  it  to  be  as  great  as  24° ;  others 
have  reduced  it  to  16°.    There  is  also  a  variation  in  different  latitudes ; 
18°  is  the  mean  value. 

b.  If  the  earth's  atmosphere  were  more  extensive  than  it  is,  the 
twilight  would  of  course  be  longer,  since  the  sun  would  not  cease  to 
illuminate  the  higher  portions  of  the  atmosphere  until  more  than  18° 
below  the  horizon  ;  and  if  the  atmosphere  were  less  extensive,  the 
reverse  of  this  would  be  the  case.     Knowing  therefore  the  depression 
of  the  sun  (18°)  requisite  for  the  cessation  of  twilight,  we  can  calcu 
late  the  extent  or  height  of  the  atmosphere.      Thus  computed,  it  is 
about  40  miles. 

QUESTIONS.— 118.  What  is  the  duration  of  twilight  at  different  places  ?  Where  is  there 
constant  twilight?  a.  Duration  of  twilight  at  the  equator?  At  the  poles?  119. 
When  does  twilight  cease  ?  «.  Diversities  of  estimate  ?  b.  What  can  we  find  by  know* 
ing  this  fact  ?  c.  Why  is  the  duration  of  twilight  different  at  different  places  ?  Explain 
by  the  diagram  (Fig.  52). 


PROBLEMS     FOR    THE     GLOBE. 


79 


P' 


c.  If  the  circles  of  daily  motion  were  at  all  places  equally  inclined 
to  the  horizon,  the  duration  of  twilight  would  everywhere  be  the  same  ; 
since  the  earth  would  always  have  to  turn  the  same  amount  to  bring 
the  sun  18°  degrees  below  the  horizon  ;  but  the  more  oblique  the  circles 
are,  the  farther  the  earth  has  to  turn,  and  hence  the  twilight  is  longer 
the  nearer  we  go  to  the  poles. 

Let  the  large  circle  repre-  FiK-  52. 

sent  the  celestial  sphere,  e  the 
earth  in  the  centre ;  P  H  the 
altitude  of  the  pole  in  one  po- 
sition of  the  sphere,  and  P'  H 
its  altitude  in  one  less  oblique; 
E  E  and  E'E'  the  equinoctial 
in  each,  and,  of  course,  the 
direction  of  the  circles  of 
daily  motion.  In  the  more 
oblique  sphere,  that  is,  at 
the  place  in  the  more  north 
era  latitude,  the  celestial 
sphere,  or  which  is  the  same 
thing,  the  earth,  would  have 
to  turn  a  distance  on  the 
diurnal  circle,  equal  to  e  a, 
to  bring  the  sun  18°  below 

the  horizon;  while  in  the  other  position,  the  sun  would  reach  the 
same  point  of  depression  when  the  sphere  had  turned  only  e  b.  Thus  we 
see  the  nearer  the  perpendicular  the  diurnal  circles  are,  the  shorter  the 
twilight ;  while  the  more  oblique  they  are,  the  longer  the  twilight. 

PROBLEMS  FOR  THE  TERRESTRIAL  GLOBE. 
PROBLEM  I. — To  find  on  what  two  days  of  the  year  the 
sun  is  vertical  at  any  place  in  the  Torrid  Zone :  Turn  the 
globe  around,  and  observe  what  two  points  of  the  ecliptic 
pass  under  the  degree  of  the  brass  meridian  corresponding 
to  the  latitude  of  the  place ;  and  the  days  opposite  these 
points  in  the  circle  of  signs  will  be  those  required. 

EXAMPLES. 
On  what  two  days  of  the  year  is  the  »un  vertical  at 

1.  BOMBAY  ?  Ana.  May  15th  and  July  29th. 

2.  BAHIA?  Ana.  Oct.  28th  and  Feb.  14th. 


OF   TWILIGHT. 


80  PROBLEMS     FOB    THE     GLOBE. 

PROBLEM  II. — To  find  the  time  of  the  sun's  rising  and 
setting,  and  the  length  of  the  day,  at  any  place,  and  on  any 
day  in  the  year :  Elevate  the  pole  as  many  degrees  as  are 
equal  to  the  latitude  of  the  place,  find  the  sun's  place,  bring 
it  to  the  meridian,  and  set  the  index  to  twelve.  Then  turn 
the  globe  till  the  sun's  place  is  brought  to  the  eastern  edge 
of  the  horizon,  and  the  index  will  show  the  time  of  the 
sun's  rising ;  bring  it  to  the  western  edge,  and  the  index 
will  show  the  time  of  the  sun's  setting.  Double  the  time 
of  its  setting  will  be  the  length  of  the  day ;  and  double  the 
time  of  its  rising,  the  length  of  the  night. 

NOTE. — The  globe,  of  course,  only  shows  this  approximatively.  A  cor- 
rection would  also  be  required  for  refraction. 

EXAMPLES. 

At  what  time  does  the  sun  rise  and  set,  and  what  is  the  length  of  the 
day  and  night, 

1.  At  LONDON,  July  17th  ?  Ans.  Sunrises  at  4,  and  sets  at  8  ;  length 

of  day,  16  hours  ;  night,  8  hours. 

2.  At  NEW  YORK,  May  25th  ?    Ans.  Sun  rises  at  4J,  and  sets  at  7£  ; 

length  of  day,  14£  hours ;  night,  9^  hours. 

PROBLEM  III. — To  find  the  length  of  the  longest  and 
shortest  days  and  nights  at  any  place  not  within  either  of 
the  polar  circles :  Find,  by  the  preceding  problem,  the  length 
of  the  day  and  night  at  the  time  of  the  northern  solstice, 
if  the  place  be  north  of  the  equator,  and  at  the  time  of  the 
southern  solstice,  if  it  be  south  of  the  equator ;  and  this 
will  be  the  longest  day  and  shortest  night.  The  longest 
day  is  equal  to  the  longest  night,  and  the  shortest  day  to 
the  shortest  night. 

EXAMPLES. 
What  is  the  length  of  the  longest  and  the  shortest  day 

1.  At  NEW  YORK  ?    Ans.  Longest  day,  14  hours  56  min. ;  shortest 

day,  9  hours  4  min. 

2.  At  BERLIN  ?    Ans.  Longest,  16£  hours  ;  shortest  7£  hours. 


PROBLEMS  FOR  THE  GLOBE.         81 

PROBLEM  IV. — To  find  the  beginning,  end,  and  duration 
of  constant  day  at  any  place  within  either  of  the  polar  circles : 
Take  a  degree  of  declination  on  the  brass  meridian  equal 
to  the  polar  distance  of  the  place,  then  on  turning  the  globe 
around,  the  two  points  on  the  ecliptic  which  pass  under  that 
degree  will  be  the  places  of  the  sun  at  the  beginning  and 
end  of  constant  day.  Find  the  day  of  the  month  corre- 
sponding to  each,  and  it  will  be  the  times  required.  The  in- 
terval between  these  dates  will  be  the  duration  of  constant 
day. 

Constant  night  is  equal  to  constant  day  at  a  place  situated  under  the  cor- 
responding parallel  in  the  other  hemisphere.  Hence,  to  find  the  duration 
of  constant  night  at  a  place  in  north  latitude,  find  the  length  of  constant 
day  at  a  place  having  the  same  number  of  degrees  of  south  latitude. 

EXAMPLES. 

Find  the  beginning,  end,  and  duration  of  constant  day  and  night  at 

1.  NORTH  CAPE.    Ans.  Constant  day  begins  May  14th,  ends  July 

30th ;  duration,  77  days.  Constant  night  begins 
November  25th,  ends  January  27th  ;  duration,  73 
days. 

2.  NORTH  POLE.    Ans.  Constant  day  begins  March  20th,  ends  Sep- 

tember 23d  ;  duration,  187  days.  Constant  night 
begins  September  23d,  ends  March  20th ;  dura- 
tion, 178  days. 

PROBLEM  V. — To  find  the  duration  of  twilight  at  anyplace 
not  within  either  of  the  polar  circles :  Elevate  the  pole  equal  to 
the  latitude,  find  the  sun's  place,  bring  it  to  the  western  edge 
of  the  horizon,  and  note  the  time  shown  by  the  index.  Then 
screw  the  quadrant  over  the  place,  and  bring  its  graduated 
edge  to  the  sun's  place ;  turn  the  globe  till  the  sun's  place 
is  shown  by  the  quadrant  to  be  18°  below  the  horizon,  and 
the  time  passed  over  by  the  index  will  be  the  duration  of 
twilight. 


82  THE    SEASONS. 

EXAMPLES. 

1.  What  is  the  duration  of  twilight  at  LONDON,  September  23d  ? 

Ans.  2  hours. 

2.  What  is  it  at  DRESDEN,  April  19th?    Ans.  2  hours  15  minutes. 


SECTION    V. 

THE    SEASONS. 

120.  The  SEASONS  are  the  four  nearly  equal  divisions  of 
the  year,  which  are  distinguished  from  one  another  by  the 
comparative  length  of  the  day  and  night,  and  the  difference 
in  the  amount  of  heat  received  from  the  sun. 

121.  The  CAUSES  OF  THE  SEASONS  are  the  inclination  of 
the  axis  of  the  earth  to  the  plane  of  its  orbit,  and  its  revo- 
lution around  the  sun ;  and  the  vicissitudes  are  regular,  that 
is,  always  hhe  same  from  year  to   year,  because  the  axis 
always  points  in  the  same  direction,  or  remains  parallel  to 
itself. 

a.  These  four  periods,  called  Spring,  Summer,  Autumn,  and  Winter 
are  marked  and  limited  by  the  arrival  of  the  sun  at  the  vernal  equi- 
nox, northern  solstice,  autumnal  equinox,  and  southern  solstice,  respect- 
ively. The  following  statements  will  be  understood  by  an  inspection 
of  the  accompanying  illustration  (Fig  53) : 

1.  Sun  in  the   Northern  Solstice. — When  the  sun  enters  Cancer 
(northern  solstice),  the  north  pole  is  presented  to  the  sun  ;  and  summer 
is  produced  in  the  northern  hemisphere,  because  the  rays  of  the  sun 
fall  directly  upon  that  part  of  the  earth  ;  while  winter  occurs  in  the 
southern  hemisphere,  because  there  the  sun's  rays  are  oblique ; 

2.  Sun  in  the  Southern  Solstice. — When  the  sun  enters  Capricorn 
(southern  solstice),  the  south  pole  is  presented  to  the  sun,  and  summer 
occurs  in  the  southern  hemisphere,  and  winter  in  the  northern ; 

QUESTIONS.— 120.  "What  are  the  seasons  ?  111.  How  caused  ?  n.  How  limited  ? 
What  are  the  seasons  when  the  sun  enters  Cancer  ?  When  the  sun  enters  Capricorn  ? 


THE    S  EASONS. 
Fig.  53- 


83 


THE  SEASONS. 

3.  Sun  in  the  Equinoxes. — When  the  sun  enters  either  of  the  equi- 
noxes, the  earth's  axis  leans  sidewise  to  it,  and  the  rays  are  direct  to 
the  equator,  and  equally  oblique  on  both  sides  of  it.     Consequently, 
there  is  neither  summer  nor  winter ;  but  spring  in  that  hemisphere 
which  the  sun  is  entering,  and  autumn  in  that  which  it  has  left ; 

4.  Hence,  when  the  sun  enters  Aries  (vernal  equinox),  there  is  spring 

QUESTIONS.— When  it  is  at  either  of  the  equinoxes  ?    When  it  enters  Aries  ?    Libra  ? 


84  THE    SEASONS. 

in  the  northern  hemisphere,  and  autumn  in  the  southern ;  and  when 
it  enters  Libra  (autumnal  equinox),  the  reverse  is  the  case. 

6.  By  the  sun's  entering  a  sign,  is  meant  its  appearing  at  the  first 
point  of  that  sign  in  the  ecliptic ;  the  earth,  as  seen  from  the  sun, 
would  appear,  of  course,  at  the  first  point  of  the  opposite  sign. 

la  the  inner  circle  of  the  diagram  (Fig.  53),  containing  the  names  of  the 
months,  the  dates  give  the  times  at  which  the  earth  enters  the  correspond- 
ing signs  in  the  outer  circle.  Of  course,  the  sun,  at  these  dates  enters  the 
opposite  signs. 

122.  SUMMER  is  caused  by  the  rays  of  the  sun  being  more 
nearly  perpendicular  than  in  the  other  seasons,  so  that  the 
same  part  of  the  earth's  surface  receives  a  greater  quantity 
of  light  and  heat.  WINTER  is  caused  by  the  greater  obliquity 
of  the  sun's  rays,  in  consequence  of  which  the  same  quan- 
tity of  light  and  heat  is  diffused  over  a  greater  surface. 

Fig.  54. 


SUMMER   AND  WINTKB  BAYS. 


In  Fig.  54,  it  will  be  observed  that  the  same  quantity  of  rays  that  covers 
the  north  polar  circle,  when  they  are  direct,  covers  the  whole  space  from 
the  antarctic  circle  to  the  equator,  when  they  are  oblique. 

123.  The  seasons  are  not  precisely  of  equal  length,  be- 
cause the  earth  revolves  in  an  elliptical  orbit,  and  conse- 
quently passes  through  one  half  of  it  in  less  time  than  the 
other. 

«.  The  perihelion  of  the  orbit  is  in  the  llth  degree  of  Cancer,  its 
longitude  being  100°  21' ;  so  that  when  the  earth  is  at  this  point,  the 

QUESTIONS.— ft.  What  is  meant  by  the  sun's  entering  a  sign?  122.  How  is  summer 
caused?  Winter?  Explain  by  the  diagram.  123.  Are  the  seasons  of  equal  length? 
a.  Explain  the  cause. 


THE    SEASONS. 


85 


sun  is  in  the  llth  degree  of  Capricorn,  January  1st.  Thus,  the  earth 
passes  its  perihelion,  and  is,  consequently,  nearest  to  the  sun,  in  winter ; 
and  the  time  occupied  by  the  sun  in  going  from  Libra  to  Aries,  that  is, 
from  the  beginning  of  autumn  to  the  beginning  of  spring,  is  shorter  by 
about  eight  days  than  the  time  from  Aries  to  Libra,  or  from  spring  to 
autumn  again.  The  seasons  are,  of  course,  reversed  in  the  southern 
hemisphere. 

b.  The  duration 
of  the  seasons,  re- 
spectively, is  as  fol- 
lows :  Spring,  92.9 
days ;  Summer, 
93.6  days ;  Autumn, 
89.7 days;  Winter, 
89  days.  Thus,  «- 
Spring  and  Sum- 
mer contain  186£ 
days ;  and  Autumn 
and  Winter,  178f- 
days;  Winter  be- 
ing the  shortest 
season,  and  Sum- 
mer the  longest. 

Fig.  55  will  render 
this  clear  to  the  un- 
derstanding of  the  student.    The  diagram  shows  the  position  of  the  earth 
when  the  sun  is  at  the  solstices  and  equinoxes,  respectively,  and  the  unequal 
portions  into  which  the  orbit  is  divided  by  the  lines  joining  these  points, 
corresponding  to  the  unequal  periods  of  time  mentioned  above. 

f.  Motion  of  the  Line  of  Apsides. — The  line  of  apsides  of  the 
earth's  orbit  does  not  always  remain  in  the  same  position  in  space,  but 
slowly  moves  toward  the  east,  about  11J"  every  year  ;  hence,  making  a 
complete  circuit  in  about  110,000  years.  But  the  equinoxes  are  moving 
the  other  way  about  50"  every  year  (Art.  105 ),  so  that  the  angular  dis- 
tance between  the  perihelion  and  the  equinox  increases  annually  about 
1'  (more  exactly,  62") ;  that  is  to  say,  the  longitude  of  the  perihelion  is 
about  1'  greater  at  every  successive  year. 


UNEQUAL   LENGTH   OF  SEASON* 


QUESTIONB.— 6.  What  is  the  duration  of  each  season  ?    Explain  by  the  diagram. 
c.  What  motion  has  the  line  of  apsides  ?    Its  effect  on  the  perhelion  T 


86  THE    SEASONS. 

(1.  Length  of  the  Seasons  Variable. — The  comparative  length  of  the 
seasons  is,  therefore,  not  the  same  at  different  periods.  About  6,000 
years  ago,  the  aphelion  must  have  coincided  with  the  vernal  equinox ; 
and  hence,  the  seasons  of  summer  and  autumn  must  have  been  equal, 
and  also  those  of  spring  and  winter  ;  and  the  former  must  have  been 
shorter  than  the  latter.  About  10,500  years  ago,  the  earth  was  nearest 
to  the  sun  in  summer,  and  farthest  from  it  in  winter,  and  the  seasons 
of  spring  and  summer  were  the  shortest,  and  those  of  autumn  and 
winter  the  longest.  This  would  make  the  summers  of  the  northern 
hemisphere,  according  to  the  calculations  of  Sir  John  Herschel,  23° 
hotter  than  they  now  are.  [Let  the  student  modify  the  diagram 
(Fig.  55)  so  as  to  show  each  of  these  positions  of  the  line  of  apsides]. 

e.  Eccentricity  Variable. — The  seasons  are  also  affected,  during 
very  long  periods,  by  the  variation  in  the  eccentricity  of  the  earth's 
orbit.  At  present  this  is  diminishing  at  the  rate  of  about  -^fan,-  of  the 
mean  distance  in  a  century ;  that  is,  about  36^  miles  every  year  ;  and 
as  the  major  axis  of  the  orbit,  and,  of  course,  the  mean  distance,  always 
remain  the  same,  we  are,  therefore,  every  year  36^  miles  farther  from 
the  sun  in  perihelion,  and  36 1  miles  nearer  to  it  in  aphelion,  than  during 
the  preceding  one.  If  this  change  continued  for  ages,  the  orbit  would 
finally  become  a  circle,  and  the  seasons  would  be  greatly  changed ; 
but  Lagrange,  a  famous  French  mathematician,  demonstrated  that 
it  takes  place  only  within  very  narrow  limits,  at  the  rate  above  men- 
tioned. If  the  eccentricity  has  continued  to  diminish  for  80,000  years 
at  this  rate,  at  the  commencement  of  that  period,  it  must  have  been 
three  times  as  great  as  at  present,  or  about  4^  millions  of  miles  instead 
of  one  million  and  a  half.  The  aphelion  distance  must  then  have 
been  96  millions,  and  the  perihelion  distance  87  millions.  Now,  the 
intensity  of  the  solar  heat  varies  inversely  as  the  square  of  the  dis- 
tance ;  and  the  heat  of  the  interplanetary  spaces  has  been  estimated  at 
490°  below  zero.  Hence,  if  we  estimate  the  average  winter  heat  at 
39°,  the  amount  of  heat  received  from  the  sun  must  be  529°  ;  and 
962 :  932 : :  529°  :  496°.  Hence,  if  the  aphelion  distance  were  96  mil- 
lions of  miles  instead  of  93  millions,  the  average  winter  heat  would 
be  reduced  to  6°,  or  26°  below  the  freezing  point. 

124.  The  DIFFERENCE  OF  TEMPERATURE  in  the  seasons  is 


QUFSTIONB.  —  d.  Effect  of  the  motion  of  the  apsides  on  the  length  of  the  seasons  ?    124. 
What  causes  the  difference  of  temperature  during  the  seasons  ? 


THE    SEASONS.  87 

not  only  dependent  upon  the  direction  of  the  sun's  rays, 
but  also  upon  the  comparative  duration  of  day  and  night. 
Thus,  summer  occurs  when  the  days  are  longest,  and  win- 
ter when  they  are  shortest 

a.  All  parts  of  the  earth's  surface  are  not  affected  alike  by  the  cir- 
cumstances which  produce  the  seasons.     Those  parts  of  the  earth  at 
which  the  sun  may  be  vertical  have  the  greatest  heat ;  those  parts  at 
which  there  may  be  constant  night  have  the  greatest  cold ;  and  the 
parts  between  these  have  a  degree  of  heat  and  cold  not  so  extreme  as 
either.    Hence,  the  earth's  surface  has  been  divided  into  five  portions, 
called  Zones. 

b.  The  boundaries  of  the  zones  must  be  the  circles  which  limit  the 
decimation  of  the  sun,  north  and  south,  and  those  within  which  there 
may  be  constant  day  or  night ;  that  is,  the  tropics  and  polar  circles. 

125.  The  ZONES  are  the  five  divisions  of  the  earth's  sur- 
face bounded  by  the  tropics  and  polar  circles.    They  are 
called   the   Torrid,  North    Temperate,   South   Temperate, 
North  Frigid,  and  South  Frigid  Zones. 

126.  The  TORRID  ZONE  includes  the  space  between  the 
tropics,  the  equator  passing  through  the  middle  of  it.    It  is 
47  degrees  wide. 

127.  The    TEMPERATE    ZONES    are  Pie-  56- 
those  which  are  included  between  the 

tropics  and  polar  circles.  The  north- 
ern is  called  the  North  Temperate 
Zone;  and  the  southern,  the  South 
Temperate  Zone.  Each  is  43  degrees 
wide. 

128.  The  FRIGID  ZONES  are  those 

included    within     the    polar    circles.  ™B  ZONE8> 

That  in  the  arctic  circle  is  called  the  North  Frigid  Zone ; 

QUESTIONS.— a.  Why  has  the  earth's  surface  been  divided  into  zones?  125.  Define 
the  zones.  How  named?  126.  Where  is  the  torrid  zone?  127.  Where  are  the  tern 
perate  zones  ?  128.  The  frigid  zones  ? 


THE    EAKTH. 


that  in  the  antarctic  circle,  the  South  Frigid  Zone.    Each 
extends  23^  degrees  from  the  pole,  and  is  47  degrees  across. 


SECTION   VI. 


THE  FIGUEE  AND  SIZE  OF  THE  EABTH. 

129.  THE  FIGURE  OF  THE  EARTH  is  that  of  an  oblate 
spheroid,  differing  but  slightly  from  a  perfect  sphere. 

a.  Proofs  that  the  Earth  is  Spheroidal.— Several  and  diverse 
proofs  may  be  given  to  establish  tkis  fact. 

1.  The  effect  of  the  centrifugal  force  would  necessarily  give  it  this 
form ;  for,  since  this  force  causes  bodies  to  fly  off  from  the  centre  of 
motion,  the  water,  or  any  other  yielding  materials  of  which  the  earth 
is  composed,  would  recede  as  far  as  possible  from  the  axis  of  rotation, 
and  thus  passing  from  the  poles  to  the  equator,  cause  the  earth  to 
bulge  out  at  those  parts.  Sir  Isaac  Newton,  from  this  consideration, 
very  nearly  ascertained  the  amount  of  oblateness  in  the  earth's  figure, 
before  any  actual  discovery  of  it  had  been  made. 


Fig.  57. 


to  become  elliptical  in  form. 

2.  The  attraction  exerted  by  tht 
tor  than  at  any  other  part,  and 
toward  either  of  the  poles.  This 


This  change  in  the  form 
of  a  rotating  body  may  be 
illustrated  by  an  apparatus 
represented  in  Fig.  57.  This 
consists  of  one  or  more  cir- 
cular hoops  of  an  elastic  ma- 
terial, fastened  at  the  lower 
end  of  the  axis,  but  free  to 
move  up  and  down,  at  the 
upper  end.  When  set  in 
rapid  rotation,  they  lose 
their  circular  form  and  are 
bulged  out  at  the  points 
farthest  from  the  axis,  so  as 


!  earth  at  its  surface  is  less  at  the  equa- 
increases  as  we  go  from  the  equator 
is  shown  by  a  pendulum's  vibrating 


QUESTIONS.— 129.  What  is  the  figure 
Illustrate  it  and  explain  by  the  diagram. 


of  the  earth?     «.  What  is  the  first  proof? 
What  is  the  second  proof? 


THE     EARTH. 


89 


Fig.  58. 


less  rapidly  at  the  equator  than  at  places  nearer  the  poles ;  and  this 
can  be  accounted  for  only  by  supposing  that  the  equatorial  parts  of  the 
earth  are  the  farthest  from  its  centre,  and  the  poles  the  nearest  to  it ; 
since  the  attraction  of  gravitation  diminishes  as  the  distance  increases. 
3.  The  length  of  a  degree  on  the  meridian  is  different  in  different 
latitudes,  showing  a  variation  in  the  curvature  of  the  earth's  surface  at 
different  parts.  If  the  earth  were  an  exact  sphere,  the  meridians  would 
be  perfect  circles,  and  consequently  of  the  same  curvature  at  every  part ; 
hence,  if  we  find,  by  exact  measurement,  that  the  curvature  is  not  the 
same,  we  know  that  they  are  not  exact  circles.  This  is  what  has  been 
ascertained.  The  length  of  a  degree  on  the  meridian  has  been  measured 
at  different  latitudes  ;  and  it  has  been  found  that  it  is  longer  the  nearer 
we  go  to  the  poles,  showing  that  the  earth  is  flattened  at  these  parts. 

Let  the  ellipse,  Fig.  58,  repre- 
sent the  form  of  the  earth.  Since 
the  curvature  at  P  is  much  less 
than  that  at  E,  the  radius  of  the 
curve  a  b  will  be  longer  than  that 
of  c  d  ;  hence,  if  the  angle  a  o  b  is 
equal  to  the  angle  c  m  d,  the  arc  a  6 
which  is  farther  from  the  centre 
than  c  d,  must  be  the  longer.  Of 
course,  this  would  be  equally  true 
of  an  angle  of  1° ;  and  thus,  the 
arc  subtending  one  degree  of  an- 
gular measurement  at  the  poles 
must  be  longer  than  the  corre- 
sponding arc  at  the  equator,  if  the  earth  is  spheroidal. 

b.  To  Find  the  Size  of  the  Earth. — The  angular  distance  of  two 
places  situated  under  the  same  meridian,  measured  from  the  earth's  cen- 
tre, is  the  arc  of  the  meridian  contained  between  the  places.  This  angle 
is  found  by  observing  the  change  of  position,  with  respect  to  the  hori- 
zon or  zenith,  which  a  star  appears  to  undergo  when  viewed  from  two 
different  points  on  the  earth's  surface,  one  being  exactly  north  of  the 
other.  The  apparent  displacement  of  the  star  is  the  angular  distance, 
or  meridian  arc,  contained  between  the  two  places.  Then,  having 
measured  the  distance  in  miles  between  the  places,  we  can  find  by  a 

QtmmoNS.— How  is  this  fact  (shown?  What  is  the  third  proof?  Illustrate  it 
Explain  by  the  diagram.  6.  How  is  the  size  qf  the  earth  found  ?  Explain  by  the 
diagram. 


90 


THE    EARTH. 


simple  proportion,  the  circumference  of  the  earth.  For,  suppose  the 
angular  distance  is  found  to  be  2£°,  and  the  actual  distance  172.76 
miles ;  then  2£°  :  360°  : :  172.76  miles  :  24,877  miles.  This  must  be  the 
circumference  of  the  earth ;  and  dividing  24,877  miles  by  3.1416,  the 
ratio  of  the  circumference  to  the  diameter,  we  obtain  its  diameter. 

To  understand  why 
a  change  in  the  place 
of  the  spectator  causes 
a  displacement  of  the 
star,  let  E  (Fig.  59) 
represent  the  centre  of 
the  earth,  P  and  P 
places  on  the  earth,  Z 
and  Z'  the  zenith  of 
\  each  respectively,  S, 
\  the  direction  of  a  star 
situated  at  an  immense 
distance  beyond.  At 
P,  the  zenith  distance 

of  the  star  is  a  c,  or  the  angle  S  P  Z ;  at  P,  the  other  place,  it  is  6  d,  or  the 
angle  8  P  Z',  greater  than  S  P  Z  by  the  angle  e  P  d,  which  is  equal  to  the 
angle  PEP.  Thus,  the  star  appears  farther  from  the  zenith  Z'  than 
from  Z  at  P  by  the  arc  of  the  meridian,  P  P. 

130.  The  oblateness  of  the  earth's  figure  is  equal  only  to 
s  Js  part  of  its  diameter,  or  26^  miles. 

a.  So  small  is  this  variation  from  an  exact  sphere,  that  if  a  body 
were  made  of  the  precise  form  of  the  earth,  having  its  longest  diame- 
ter three  feet  in  length,  the  shortest  would  be  only  one-eighth  of  an 
inch  less, — an  amount  entirely  imperceptible. 

6.  The  longest  diameter  of  the  earth  is  7,925|  miles ;  the  shortest 
diameter  7,899 ;  the  mean  diameter  7,912  miles. 

131.  The  spheroidal  figure  of  the  earth  is  the  cause  of  the 
precession  of  the  equinoxes. 

a.  Precession  Explained. — For  since  this  excess  of  matter  at  the 
equator  is  situated  out  of  the  plane  of  the  ecliptic,  the  attraction  of 

QUESTIONS. — 130.  What  is  the  degree  of  oblateness  of  the  earth  ?  Illustration  ? 
b.  What  are  the  exact  dimensions  of  the  earth  ?  131.  What  does  the  spheroidal  figure 
of  the  earth  cause  ?  a.  Explain  how  precession  is  caused  ? 


THE    EARTH  91 

the  sun  and  moon  acts  obliquely  upon  it,  and  thus  tends  to  draw  the 
planes  of  the  equinoctial  and  ecliptic  together ;  which  tendency,  by 
the  rotation  of  the  earth  on  its  axis,  is  converted  into  a  sliding  move- 
ment, as  it  were,  of  one  circle  upon  the  other,  both  preserving  very 
nearly  the  same  inclination. 

Fig.  60, 


Thus  (Fig.  60)  the  attraction  of  the  sun,  acting  obliquely  upon  the  protu- 
berance, or  excess  of  matter,  at  E  and  E',  tends  to  draw  it  toward  the  plane 
of  the  ecliptic ;  and  this  it  would  finally  accomplish  were  the  earth's  rota- 
tion suspended ;  so  that  the  plane  of  the  equator  would  be  made  to 
coincide  with  that  of  the  ecliptic.  But  the  effect  is  a  sliding  of  the  equator 
over  the  line  of  the  ecliptic,  and  thus  a  change  of  the  points  of  inter- 
section. 

b.  Revolution  of  the  Poles. — Since  the  equator  moves  round  on 
the  ecliptic,  the  poles  of  the  earth  must  revolve  around  those  of  the 
ecliptic,  and  consequently  change  their  apparent  position  among  the 
stars.    Hence,  the  star  which  is  now  so  near  the  north  celestial  pole 
will  not  always  be  the  pole-star ;  but  in  about  13,000  years,  that  is, 
one-half  the  period  of  an  entire  revolution,  will  be  47°  from  it. 

c.  Why  the  Equinoctial  Points  move  toward  the  West. — It  may 
not  be  obvious  why  the  equinoctial  points  move  toward  the  west ;  but 
perhaps  the  following  diagram  and  explanation  will  render  it  clear : 

Let  E  E  (Fig.  61)  represent  the  equator,  and  e  e  the  ecliptic,  A  the  first 
degree  of  Aries,  or  vernal  equinox ;  a  6  the  amount  of  force  exerted  to 
draw  the  equator  toward  the  ecliptic  in  a  given  time,  and  a  d  the  amount 
of  rotation  performed  in  that  time.  By  the  principle  of  resultant  motion, 
the  excess  of  matter  and,  of  course,  the  earth  with  it,  would  move  in  the 


QUKSTIONS.— ft.  Effect  on  the  position  of  the  poles?    c.  Why  does  the  equinox  move 
toward  the  west  ?  Explain  by  the  diagram  (Fig.  61). 


diagonal  a  c,  thus  changing  the  direction  of  the  equator  from  E  E  to  g  h^ 
and  causing  the  point  of  intersection  to  recede  from  A  to  A'.  It  will  be 
obvious  that  the  angle  of  inclination  at  A  must  be  very  nearly  equal  to 
that  at  A'. 

d.  Obliquity  of  the  Ecliptic  Variable. — There  is  a  very  slow  dimi- 
nution of  the  obliquity  of  the  ecliptic,  amounting  to  46V  m  a  century. 
At  present  (1867),  the  obliquity  is  23°  27'  24".  The  limit  of  the  varia- 
tion is  1°  21',  to  pass  through  which  arc  it  requires  about  10,000  years. 


SECTION    VII. 


TIME. 

132.  The  apparent  motions  of  the  sun  and  stars,  caused 
by  the  real  motions  of  the  earth,  afford  standards  for  the 
measurement  of  time. 

133.  The  time  which  elapses  between  a  star's  leaving  the 
meridian  of  a  place  until  it  returns  to  it  again  is  called  a 

SIDEREAL*  DAY. 

d.  This  is  the  time  of  one  complete  revolution  of  the  celestial 
sphere,  and  is  the  exact  period  of  one  rotation  of  the  earth  on  its  axis. 
It  is  an  absolutely  uniform  standard,  having  undergone  not  the 
slightest  appreciable  change  from  the  date  of  the  earliest  recorded 


*  From  the  Latin  word  sidus,  which  means  a  star. 

QTTESTIONS. — d.  What  change  takes  place  in  the  obliquity  of  the  ecliptic  ?    132.  What 
are  the  standards  for  measuring  time  ?    133.  What  is  a  sidereal  day  ?    a.  Is  it  uniform  f 


TIME. 


93 


observations.     Indeed,  it  is  the  only  absolutely  uniform  motion  ob- 
served in  the  heavens. 

134.  A   SOLAR  DAY  is  the  period  which   elapses  from 
the  sun's  leaving  the  meridian  of  a  place  until  it  returns  to 
it  again. 

a.  As  the  sun  is  constantly  changing  its  place  among  the  stars, 
owing  to  the  annual  revolution  of  the  earth,  this  period  must  be 
longer  than  a  sidereal  day  ;  for  the  sun  having  moved  toward  the  east 
during  the  time  of  a  rotation,  the  earth  must  turn  farther  in  order  to 
bring  the  place  again  into  the  same  relative  position  with  the  sun. 
This  will  be  understood  by  examining  the  annexed  diagram. 

Let   1    represent  Fig  62 . 

the  earth  in  one  po- 
sition of  its  orbit, 
and  2  the  position 
to  which  it  advances 
during  one  day ;  P, 
the  place  at  which 
the  sun  is  on  the 
meridian  at  1;  P', 
the  same  place  after 
one  complete  rota- 
tion, as  shown  by 
the  parallel  P'  8. 
It  will  be  evident 
that  in  order  to 
bring  P'  under  the 
meridian,  so  that 
the  sun  may  appear 
to  cross  it,  the  earth 
will  have  to  turn  a 
space  represented 
by  the  arc  P'  M,  which  will  make  the  solar  day  so  much  longer  than  the 
sidereal  day. 

135.  The  solar  day  exceeds  the  sidereal  day  by  an  average 
difference  of  four  minutes. 


QTTKBTIONB. — 134.  What  is  a  solar  day  ?    «.  Why  are  the  solar  days  longer  than  the 
sidereal  ?    Explain  by  the  diagram.    135.  What  is  the  average  difference  ? 


94 


TIME. 


136.  Owing  to  the  variable  motion  of  the  earth  in  its 
orbit,  and  the  obliquity  of  the  ecliptic,  this  difference  is  not 
the  same  throughout  the  year ;  and  consequently  the  solar 
days  are  of  unequal  length. 

Why  the  Solar  Days  are  Unequal.— The  first  cause  assigned  for 
the  inequality  of  the  solar  days  will  be  easily  understood,  by  referring  to 
Fig.  62 ;  since  it  will  be  at  once  apparent  that  the  length  of  the  arc  P'  M 
must  depend  upon  the  length  of  the  interval  between  1  and  2.  If  these 
intervals  vary,  the  arcs  which  represent  the  excess  over  a  rotation  turned 
by  the  earth  in  order  to  bring  the  sun  on  the  meridian,  must  also  vary,  and 
in  the  same  proportion.  Hence,  they  must  be  longest  when  the  earth  is 
in  perihelion,  and  shortest  when  it  is  in  aphelion. 

Fig.  63. 

The  second  cause, 

namely,  the  obliquity 
of  the  ecliptic,  needs 
an  independent  illus- 
tration:—Let  API 
(Fig.  63)  represent 
the  northern  hemi- 
sphere; A  E  I  the 
equinoctial,  and  A  e 
I  the  ecliptic.  Let 
the  ecliptic  be  divid- 
ed into  equal  por- 
tions, A  6,  6  c,  c  df,  etc.,  and  draw  meridians  through  the  points  of  division, 
intersecting  the  equinoctial  in  B,  C,  D,  etc.  The  divisions  of  the  ecliptic 
will  be  equal  arcs  of  longitude,  and  the  divisions  of  the  equinoctial  will  be 
the  corresponding  arcs  of  right  ascension,  and  hence  passed  over  by  the  sun 
in  equal  periods  of  time.  These  arcs  of  right  ascension,  it  will  be  apparent, 
are  not  equal ;  for  A  6,  which  is  oblique  to  A  B,  must  subtend  a  smaller  arc, 
A  B,  than  d  e  which  is  nearly  parallel  to  its  arc  D  E.  Thus  the  arcs  of  right 
ascension  are  shortest  at  the  equinoxes,  and  longest  at  the  solstices; 
while  the  divisions  coincide  at  all  these  four  points. 

137.  A  MEAN  SOLAR  DAY  is  the  average  of  all  the  solar 
days  throughout  the  year.  It  is  divided  into  twenty-four 
hours,  and  commences  when  the  sun  is  on  the  lower  meridian, 
that  is,  at  midnight. 


QUESTIONS.—  136.  Why  are  the  solar  days  unequal?    Explain  by  the  diagrams. 
What  is  a  mean  solar  day  ? 


137. 


TIME.  95 

a.  Because  used  for  the  general  purposes  of  civil  and  social  life,  it 
is  also  called  the  civil  day.  Clocks  are  regulated  to  show  its  beginning 
and  end,  and  the  equal  division  of  it  into  hours,  minutes,  and  seconds. 
As  already  stated,  it  is  four  minutes  longer  than  a  sidereal  day. 

ft.  If  the  solar  days  were  equal  in  length,  the  sun  would  always  be 
on  the  meridian  at  12  o'clock  ;  that  is,  apparent  noon  would  coincide 
with  mean  noon — the  noon  of  the  clock.  But  this  is  not  the  case,  and 
therefore  to  make  the  observed  noon,  as  indicated  by  the  sun,  corre- 
spond with  the  noon  of  the  clock,  a  correction  has  generally  to  be 
made,  either  by  adding  or  subtracting  a  certain  amount  of  time.  This 
correction  is  called  the  equation  of  time. 

138.  The  EQUATION  or  TIME  is  the  difference  between 
apparent   and  mean  time ;  that  is,  the  difference  between 
time  as  shown  by  the  sun,  and  that  shown  by  a  well-regu- 
lated clock. 

a.  The  unequal  motion  of  the  earth  in  its  orbit  causes  the  sun  to 
be  in  advance  of  the  clock  from  aphelion  to  perihelion,  that  is,  from 
July  1st  to  January  1st ;  and  behind  it  from  January  1st  to  Jul  1st ; 
while  they  both  coincide  at  those  points.  The  obliquity  of  the  ecliptic 
causes  the  sun  to  be  in  advance  of  the  clock  from  Aries  to  Cancer, 
behind  it  from  Cancer  to  Libra,  in  advance  again  from  Libra  to  Capri- 
corn, and  behind  again  from  Capricorn  to  Aries  ;  and  makes  them 
both  agree  at  those  four  points.  To  verify  this  let  the  student  exam- 
ine Fig.  63.  When  these  two  causes  act  together,  as  is  the  case  in 
the  first  three  months  and  the  last  three  months  of  the  year,  the  equa- 
tion of  time  is  the  greatest. 

139.  The  equation  of  time  is  greatest  in  the  beginning  of 
November,  the  sun  being  then  about  16|  minutes  in  advance 
of  the  clock. 

a.  Hence,  to  deduce  true  noon  from  apparent  noon,  at  that  time  it  is 
necessary  to  subtract  16',  minutes  from  the  observed  time.  The  sun  is  at 
the  greatest  distance  behind  the  clock  about  February  10th,  the  equation 


QUESTIONS.— a.  Why  called  a  civil  day  ?  ft.  What  is  meant  by  apparent  and  mean 
noon  ?  Do  they  coincide  ?  138.  What  is  the  equation  of  time  ?  «.  When  is  the  sun 
in  advance  of  the  clock?  When  behind  it?  139.  When  is  the  equation  of  time  the 
greatest  ? 


9G  TIME. 

being  then  14^  minutes,  and,  of  course,  to  be  added,  in  order  to  find 
the  correct  time. 

140.  Mean  and  apparent  time  coincide  four  times  a  year, 
namely ;  April  15th,  June  15th,  September  1st,  and  Decem- 
ber 24th.    The  equation  of  time  then  becomes  nothing. 

b.  To  Find  the  Equation  of  Time  by  the  Globe. — The  part  of 
the  equation  of  time  that  depends  upon  the  obliquity  of  the  ecliptic 
can  be  found  by  the  globe,  in  the  following  manner  : — Bring  the  sun's 
place  in  the  ecliptic  to  the  brass  meridian,  and  find  its  longitude  and 
right  ascension  ;  the  difference  reduced  to  time  (counting  four  minutes 
to  a  degree),  will  be  the  equation.  If  the  right  ascension  exceed  the 
longitude,  the  sun  is  slower  than  the  clock  ;  if  the  longitude  exceed 
the  right  ascension,  the  sun  is  faster  than  the  clock. 

Thus,  on  the  28th  of  January,  the  longitude  of  the  sun  is  about  308°,  the 
right  ascension  310£° ;  hence  the  sun  is  10  minutes  slower  than  the  clock. 
QUESTIONS. — What  is  the  equation  of  time  October  19th  ?    Ans.  Sun  10 

minutes  faster  than  the  clock. 

What  is  it  August  13th  ?    Ans.  Sun  8  minutes  slower  than 
the  clock. 

141.  A   SIDEREAL  YEAR  is    the    period  of  time   that 
elapses  from  the  sun's  leaving  any  star  until  it  returns  to 
the  same  again. 

a.  This  is  the  true  period  of  the  annual  revolution  of  the  earth, 
and  is  equal  to  365  days,  6  hours,  9  minutes,  9  seconds.  Owing,  how 
ever,  to  the  precession  of  the  equinoxes,  the  sun  advances  through  all 
the  signs,  from  either  equinox  to  the  same  again,  in  a  shorter  period. 

142.  A  TROPICAL  YEAR  is  the  period  that  elapses  from 
the  sun's  leaving  the  vernal  equinox  until  it  arrives  at  it 
again.    It  is  20  min.  20  sec.  shorter  than  the  sidereal  year. 

a.  Its  length  is,  therefore,  365d  5h  48m  49*  which  is  the  civil  year,  or 
the  year  of  the  calendar,  deducting  the  5h  48m  49'  ;  and  as  this  is 
very  nearly  one-fourth  of  a  day,  one  day  is  added  every  fourth  year, 

QUESTIONS.— 140.  When  is  the  equation  of  time  nothing  ?  141.  What  is  a  sidereal 
year?  142.  What  is  a  tropical  year ?  How  much  shorter  than  a  sidereal  year?  a. 
What  is  its  length  ?  What  other  names  has  it  ? 


QUESTIONS    FOB    EXERCISE.  97 

which  makes  what  is  called  leap  year,  or  bissextile.     The  tropical 
year  is  sometimes  called  an  equinoctial  or  solar  year. 

b.  The  sidereal  year  is  not  exactly  the  period  which  the  earth 
requires  to  pass  from  perihelion  to  perihelion  again,  since  the  perihe- 
lion is  moving  slowly  toward  the  east  (Art.  123,  c).  This  period  is 
called  the  anomalistic  year.  It  is  about  4^  minutes  longer  than  the 
sidereal  year. 

QUESTIONS    FOR    EXERCISE. 

These  questions  are  to  be  answered  by  applying  the  principles  explained 
in  the  preceding  sections,  and  without  the  use  of  the  globe, 

1.  What  is  the  latitude  of  the  north  pole  ? 

2.  What  is  the  latitude  of  a  place  under  the  equator  ? 

3.  New  York  is  about  49  £  degrees  from  the  north  pole  ;  what  is  its 
latitude  ? 

4.  How  many  degrees  is  it  from  the  south  pole  ? 

5.  What  is  the  latitude  of  a  place  under  the  Tropic  of  Cancer  ? 

6.  What  under  the  Antarctic  Circle?     Under  the  Tropic  of  Cap- 
ricorn? 

7.  What  is  the  greatest  altitude  of  a  heavenly  body  ? 

8.  Where  is  the  altitude  greatest  ?    Where  is  it  least  ? 

9.  If  the  zenith  distance  of  a  body  is  15°,  what  is  its  altitude  ? 

10.  How  many  degrees  wide  id  the  circle  of  perpetual  apparition  in 
the  latitude  of  New  York  ? 

11.  How  wide  is  it  at  the  north  pole  ?    At  the  equator  ? 

12.  If  the  declination  of  a  star  is  60°  N.,  does  it  ever  set  in  New  York  ? 

13.  Does  it  rise  in  latitude  30°  S.  ? 

14.  At  what  points  is  the  declination  of  the  sun  greatest  ? 

15.  At  what  points  is  its  declination  nothing  ? 

16.  What  is  the  right  ascension  of  the  sun  in  the  first  degree  of  Can- 
cer?   What  in  the  first  degree  of  Capricorn  ?    In  the  first  degree  of 
Libra  ?    In  the  vernal  equinox  ? 

17.  What  is  the  longitude  of  the  sun  in  the  summer  solstice  ?  In  the 
winter  solstice  ?    In  the  autumnal  equinox  ? 

18.  When  the  sun  is  in  either  of  the  equinoxes,  what  is  its  merid- 
ian altitude  in  New  York  ?    In  London  ?    At  Cape  Horn  ?    At  North 
Cape? 

QUESTIONS.— ft.  What  is  an  anomalistic  year  ?    Why  longer  than  a  sidereal  year  ? 


98  QUESTIONS    FOR    EXERCISE. 

19.  What  is  the  greatest  meridian  altitude  of  the  sun  in  New  York  ? 
What  is  the  least  1 

20.  If  the  declination  of  a  star  is  30°  N.,  what  is  its  meridian  alti- 
tude in  New  York  ?     Its  zenith  distance  ? 

21.  What  must  its  declination  be  to  be  seen  in  the  zenith  at  New 
York? 

22.  When  is  it  longest  day  in  New  York  ?    At  Cape  Horn  ? 

23.  If  a  star  were  seen  on  the  meridian  40°  from  the  zenith,  what 
would  be  its  altitude,  azimuth,  and  amplitude  ? 

24.  If  the  meridian  altitude  of  a  star  in  Havana  is  50°,  what  is  its 
declination  ? 

25.  What  are  the  amplitude,  azimuth,  zenith  distance,  and  altitude 
of  a  star  just  rising  15°  from  the  east? 

26.  What  is  the  right  ascension  of  the  sun  when  its  declination  is 

23FS.? 

27.  What  is  its  declination  when  its  longitude  is  90°  ? 

28.  What  is  its  right  ascension  when  its  longitude  is  180°  ? 

29.  Where  is  a  planet  situated  when  its  latitude  is  0°  ? 

30.  In  what  position  is  Mars  when  it  has  the  same  longitude  as  the 
sun? 

31.  At  what  point  of  a  planet's  orbit  is  the  centripetal  force  greatest  ? 
The  centrifugal  force  ? 

32.  If  the  inclination  of  the  earth's  axis  had  been  30°,  how  wide 
would  each  of  the  zones  have  been  ? 

33.  If  it  had  been  45°,  how  wide  would  the  torrid  zone  have  been  ? 
The  temperate  zones  ? 

34.  If  the  earth's  axis  were  perpendicular,  where  would  perpetual 
summer  prevail  ?    Perpetual  winter  ? 

35.  What  would  be  the  seasons,  if  the  earth's  axis  coincided  with 
the  plane  of  the  ecliptic  ? 

36.  Is  constant  day  as  long  at  the  south  as  at  the  north  pole  ? 


CHAPTER    VIII. 


THE    SUX. 

143.  The  SUN  is  the  source  of  light  and  heat  to  all  the 
other  bodies  of  the  solar  system,  and  the  support  of  life  and 
vegetation  on  the  surface  of  the  earth,  or  any  of  the  other 
planets. 

All  the  forces  displayed  on  our  planet,  whether  mechanical,  chem- 
ical, or  vital,  spring  from  the  sun  and  his  exhaustless  rajs ;  and  yet, 
it  is  calculated,  that  the  earth,  with  its  limited  grasp,  only  receives  the 
two  hundred  and  thirty  millionth  part  of  the  whole  force  radiated  and 
dispensed  by  this  vast  and  splendid  luminary. 

144.  The  greatest  distance  of  the  sun  from  the  earth  is 
very  nearly  93   millions  of  miles ;  and  its  least  distance 
about  90  millions ;  making  the  mean  distance,  as  previously 
stated,  about  91A  millions. 

a.  History  of  its  Discovery. — The  distance  of  the  sun  from  the 
earth  has  been,  from  the  earliest  times,  a  subject  of  close  and  earnest 
investigation  to  astronomers.  Ptolemy  and  those  contemporary  with 
him,  and  in  more  modern  times  Copernicus  and  Tycho  Brahe,  supposed 
it  to  be  equal  to  only  1200  times  the  radius  of  the  earth,  or  less  than  five 
millions  of  miles ;  Kepler  thought  it  to  be  about  fourteen  millions  of 
miles ;  Halley,  sixty -six  millions ;  and  it  was  not  until  the  middle  of 
the  last  century  (1769),  that  any  reliable  determination  of  this  impor- 
tant fact  was  reached.  This  was  accomplished  by  finding  the  horizontal 
parallax  of  the  sun  by  means  of  observations  made  at  different  parts 
of  the  earth,  of  the  transit  of.  Venus,  which  took  place  in  that  year. 

QUESTIONS.—  143.  What  is  the  sun  ?  144  What  is  its  distance  from  the  earth  ?  a. 
Opinions  of  various  astronomers  ? 


100  THE    SUN. 

b.  When  an  inferior  planet  happens  to  be  at  or  near  one  of  its 
nodes,  at  the  time  of  inferior  conjunction,  it  appears  like  a  round  black 
spot  on  the  disc  of  the  sun,  and  moves  across  it  from  east  to  west. 
This  passage  across  the  disc  is  called  a  transit.  The  transits  of  Venus 
have  been  of  very  great  interest  because  employed  to  determine  the 
solar  parallax.  The  method  will  be  explained  hereafter. 

145.  The  distance  of  the  sun  from  the  earth  is  ascertained 
by  finding  its  horizontal  parallax.  According  to  a  recent 
determination,  this  is  a  little  less  than  9". 

a.  This  has  been  found  by  a  series  of  observations  on  Mars,  made  at 
the  time  of  its  opposition  in  1860  and  1862,  it  being  in  those  years  at 
about  its  nearest  point  to  the  earth.    More  exactly  stated,  the  solar 
parallax  is  8. 94". 

b.  It  has  been  already  shown  (Art.  87, «.),  that  the  angle  of  parallax 
varies  with  the  distance.   The  method  of  determining  the  distance  from 
the  parallax  is  as  follows  : 

Fig.  64.  Let  E  (Fig.  64)  repre- 

P  sent   the  centre  of  the 

earth,  P,  a  place  on  its 
surface,  and  S,  the  cen- 
tre of  the  sun.  Then 
P  S  E  is  the  angle  of 
horizontal  parallax,  or 
the  angle  which  the  ra- 
dius of  the  earth  subtends  at  the  distance  of  the  sun.  Now,  in  every  right- 
angled  triangle,  such  as  P  S  E,  the  ratio  of  either  side  to  the  hypothenuse 
depends  on  the  angle  opposite  the  side ;  so  that  however  long  the  sides  of 
the  triangle  may  he,  the  ratio  is  the  same,  provided  the  angle  is  the  same. 
Hence,  as  tables  have  been  calculated  containing  the  ratio  of  every  possi- 
ble angle,  we  can  always  find,  by  referring  to  these  tables,  this  ratio  when 
we  know  the  angle.  In  the  triangle  S  P  E,  S  E,  the  hypothenuse,  is  the 
distance  of  the  sun,  and  P  E,  the  radius  of  the  earth,  equal  to  3956  miles. 
The  opposite  angle  P  S  E,  is  the  horizontal  parallax,  or  8.94".  For  this 
angle  we  find  the  ratio  to  be  about  .0000432;  that  is,  P  E  =  S  E  X  .0000432 ; 

PE 
and  hence  S  E  =  7)000433  ?  but  3956  *  -0000432  =  91,5 "4,074,  which  is  about 

the  mean  distance  of  the  sun. 

QUESTIONS. — 6.  What  is  a  transit  ?  145.  How  is  the  distance  of  the  sun  found  ?  ff. 
What  is  the  solar  parallax  ?  ft.  How  is  the  distance  of  the  sun  deduced  from  the  par- 
allax ? 


THE    SUK.  101 

C.  The  ratio  of  either  side  of  a  right-angled  triangle  to  the  hypoth- 
enuse,  dependent  upon  any  particular  angle,  is  called  the  sine  of  that 
angle.     Thus,  the  sine  of  30°  is  .5  or  £  ;  that  is,  if  brie  of  the,  angles  of , 
a  right-angled  triangle  is  30°,  the  side  opposite  {&&«$£&  Mty'bp  one^ 
half  the  hypothenuse.  _,• J '     ,     3      ,  tl 

(1.  Hence,  it  may  be  given  as  a  general  rule*,  th^tt  J#£e  radiid?  ofltyej> 
earth  divided  by  the  sine  of  the  Jwrizontal  parallax  of  any  body  is  equal 
to  its  distance  from  the  earth. 

NOTE. — It  is  important  that  the  student  should  keep  the  above  definition 
and  rule  in  memory,  as  they  will  be  employed  in  several  subsequent  calcu- 
lations. 

14G.  The  apparent  diameter  of  the  sun,  or  the  angle 
which  it  subtends  in  the  celestial  sphere,  is  about  32',  or  a 
little  more  than  one-ha.lf  of  a  degree. 

a.  This  is  the  mean  value  ;  the  greatest  being  32'  86'' ;  and  the  least 
31'  32",     This  variation  in  the  apparent  size  of  the  sun  is  caused  by 
the  elliptical  orbit  of  the  e^rth  ;  it  being  greatest  when  the  earth  is 
in  perihelion,  and  least  in   aphelion.     The  apparent  diameters  of  the 
sun,  at  different  periods  of  the   year,  are  measures  of  the  different 
lengths  of  the  radius-vector  of  the  earth's  orbit,  and  thus  lead  to  a 
knowledge  of  its  exact  figure. 

b.  Since  the  greatest  apparent  diameter  is  32.6r,  and  the  least  31.533', 
their  ratio  Is  as  1.034  to  1  (nearly),  and  one-half  the  difference,  or  .017, 
is  about  the  eccentricity  of  the  earth's  orbit. 

147.  The  actual  diameter  of  the  sun  is  852,900  miles,  or 
107|  times  the  diameter  of  the  earth. 

a.  This  is  found  by  a  calculation  based  upon  the  principle  of  the 
right-angled  triangle,  pxplained  in  Art.  145.  The  method  is  as  fol- 
lows : 

Let  S  (Fig.  65)  be  the  centre  of  the  sun,  E  the  place  of  the  e^irth.  Then  S  A 
E  is  a  right-angled  triangle,  in  which  the  hypothenuse  S  E  is  the  distance  of 
the  sun  from  tjie  earth.,  A  S  the  radius  pf  the  sun,  and  the^xngle  A  E  S 

QUESTIONS.— <•.  What  Is  the  vine  of  an  angle?  d.  Give  the  general  rule.  146. 
What  is  the  apnarent  diameter  of  the  sun?  a.  How  does  it  vary  ?  b.  How  may  the 
eccentricity  of  the  earth's  orbit  be  found?  147.  What  is  the  actual  diameter  of  the 
sun?  n,  TIow  found?  Explain  from  the  diagram. 


102  THE    8  UK. 

Pig-  65'  one-half  the  apparent 

diameter,  or  lt>'.  The 
ratio  corresponding  to 
this  angle,  or  the  sine 
of  the  angle,  is  .00466 ; 
hence,  91,500,COO  X 
.00466  =  426,390,  the 
semi-diameter  of  the 

sun  ;   and,  therefore,  the  diameter  is  852,780  miles,  which  is  very  nearly  its 

exact  length. 

148.  The  figure  of  the  sun  appears  to  be  that  of  a  perfect 
sphere,  no  observations  having  as  yet  detected  any  indica- 
tions of  oblateness. 

a»  Surface  and  Volume. — Since  the  surfaces  of  spheres  are  as  tlie 
squares  of  their  diameters,  and  the  volumes  as  the  cubes,  it  follows 
that  the  surface  of  the  sun  must  be  11,620  times  that  of  the  earth,  and 
its  volume  1,252,000  times  ;  or,  in  round  numbers,  one  million  and  a 
quarter  of  worlds  as  large  as  the  earth  must  be  rolled  into  one  to  form 
a  body  of  the  bulk  of  the  sun. 

149.  The  mass  of  the  sun  is  315,000  times  as  great  as 
that  of  the  earth. 

a.  The  method  of  finding  this  will  be  explained  in  a  subsequent 
article.     Since  the  volume  of  the  sun  is  1,252,000,  while  the  mass,  or 
quantity  of  matter  is  only  315,000,  as  compared  with  the  earth,  it  fol- 
lows that  the  density  of  the  sun  must  be  only  £  that  of  the  earth. 
Now,  the  earth's  density  has  been  found  by  certain  experiments  to  be 
about  5 1  (5.67)  times  that  of  water  ;  hence,  that  of  the  sun  must  be  less 
than  !$•  that  of  water  (1.42). 

b.  From  the  comparative  lightness  of  its  substance,  Kerschel  infers 
that  an  intense  heat  prevails  in  its  interior,  imparting  an  expansibility 
sufficient  to  resist  the  force  of  gravitation,  which,  otherwise,  would 
cause  the  body  to  shrink  into  smaller  dimensions. 

c.  The  volume  of  the  sun  is,  as  already  stated,  about  500  times  that 
of  all  the  planets ;  the  mass  is,  however,  about  700  times  as  great. 


QUESTIONS.— 148.  What  is  the  figure  of  the  sun  ?  n.  What  is  said  of  its  surface  and 
volume  ?  149.  What  is  its  mass  ?  «.  Its  relative  mass  and  density  ?  b.  What  is 
the  inference  drawn  by  Sir  John  Herschel?  c.  Mass  of  the  sun  compared  with  that 
of  the  planets  ? 


THE    SUN. 


103 


This  shows  that  the  density  of  the  sun  is  greater  than  the  average  density 
of  the  planets. 

150.  The  sun  rotates  from  west  to  east  on  an  axis  nearly 
perpendicular  to  the  plane  of  the  ecliptic,  the  period  ot 
rotation  being  about  25 1  days  (25d  7h  48m). 

151.  This  is  proved  by  the  spots  which  are  seen  upon  its 
disc,  and  which  appear  to  move  across  it,  occupying  about 
two  weeks  in  their  passage. 

Fig,  ee. 


A   SPOT  PASSING   ACBO88  TITE  DISC. 

<r,  A  particular  spot  which  can  be  identified  by  its  appearance  first 
appears  on  the  eastern  limb,  or  edge,  of  the  disc,  passes  across  to  the 
western  limb,  and  then  disappears  ;  but  after  about  two  weeks,  re-ap- 
pears on  the  eastern  limb,  completing  an  entire  revolution  in  about 

Pig.  67. 


THE   8TTN    ANT)   SPOTS. 


27 J  days.      But  this  must  be.  longer  than   the  period  of  a  rotation, 
because  the  earth  is  moving  in  its  orbit  in  the  same  direction.    When, 


QurgTiONS.— 150.  Does  the  sun  rotate?    151.  How  is  this  known  ?    a.  How  do  the 
spots  move  ?    Their  time  of  rotation  ?     How  to  find  the  time  of  the  sun's  rotation? 


104 


THE     SUN. 


therefore,  the  earth  has  completed  one  revolution,  the  number  of  revo- 
lutions of  the  spots  will  be  one  less  than  the  actual  number  of 
rotations  of  the  sun  for  the  time.  Hence,  365^  days  -^  2?i  days  =  13.4, 
revolutions  of  spots ;  and  13.4  +  1  =  14.4,  rotations  of  the  sun ;  there- 
fore, 365  ^  days  -r-14.4  =  25  J>  days,  the  time  of  one  rotation.  (See  Fig.  67). 

6.  It  may  appear  singular,  at  the  first  view,  to  infer  an  eastward  rota- 
tion of  the  sun  from  an  apparent  westward  motion  of  the  spots  ;  but 
it  must  be  remembered  that  the  sides  of  the  sun  and  earth  presented 
to  each  other  at  any  time  are  moving  in  opposite  directions  in  space, 
while  both  bodies  move  in  the  same  direction  in  circular  motion. 

c.  Discovery  of  the  Spots The  discovery  of  spots  on  the  solar 

disc  is  noticed  in  history  as  early  as  807  A.  D. ;  but  their  true  appear- 
ance and  extent  were  unknown  until  the  invention  of  the  telescope,  in 
the  beginning  of  the  17th  century,  at  which  time  (in  1611)  they  were 
attentively  observed  by  Galileo  and  others.  In  recent  years,  the  sun 
has  received  a  very  great  deal  of  attention  from  astronomers,  and 
many  interesting  facts  have  been  made  known  respecting  its  appearance 
and  physical  constitution. 

152.  The  inclination  of  the  sun's  axis  to  the  ecliptic  is 
7|°  ;  and,  in  consequence  of  this  inclination,  the  spots 
appear  to  move  across  the  disc  in  lines  of  various  directions 
and  form,  sometimes  being  straight  and  sometimes  curved. 


SEPTEMBER 
N 


APPUSENT   PATHS   OF    SOLAR   SPOTS. 


Fig.  68  illustrates  this.  In  March,  when  the  south  pole  is  presented  to 
the  spectator,  the  paths  assume  the  appearance  indicated  in  the  first  circle ; 
in  June,  they  are  straight  and  oblique,  because  the  observer  is  in  the  plane 


QUESTIONS. — b.  Why  do  the  spo^s   seem  to  move  from  east  to  vest?    c.  History  of 
their  discovery  f    152.  What  is  the  inclination  of  the  sun's  axis  ? 


THE    SUN.  105 

of  the  sun's  equator ;  while  in  September,  the  observer  being  north  of  its 
equator,  the  north  pole  is  turned  toward  him,  and  they  are  as  represented 
in  the  third  circle.  [The  inclination  of  the  axis  is  exaggerated  in  the 
diagram.] 

153.  APPEARANCE  OF  THE  SPOTS. — When  the  spots  are 
examined  by  means  of  a  telescope,  they  present  the  appear- 
ance of  irregular  black  patches  surrounded  with  a  dusky 
border  or  fringe,  the  whole  sometimes  encompassed  with  a 
bright  surface  or  ridge.  The  black  portion  in  the  centre  is 
called  the  umbra  or  nucleus  ;  the  dusky  border,  the  penum- 
bra ;  and  the  bright  surfaces  seen  around  the  spots,  or  by 
themselves  on  other  parts  of  the  disc,  are  called  faculce. 


— •  --— i 


BOLAB   SPOTS. 


a.  Sometimes  the  nucleus  is  absent ;  and  sometimes  spots  are  seen 
without  any  penumbra.  The  nucleus  is  not  of  a  uniform  blackness, 
but  generally  contains  an  intensely  black  spot  in  the  centre.  These 
spots  usually  appear  in  clusters,  numbering  from  two  to  sixty  or  sev- 
enty, or  even  many  more. 

154.  VARIABILITY  OF  THE  SPOTS. — The  solar  spots  con- 
stantly undergo  very  great  changes  in  number,  form,  size, 
and  general  appearance. 

QTJESTIONS.— 158.  Explain  the  appearance  of  the  spots.  «.  What  diversity  in  their 
appearance  ?  154  What  changes  do  they  undergo  ? 


106  THE    SUN. 

a.  Sometimes  the  sun's  disc  will  be  entirely  free  from  them,  and 
will  continue  so  for  weeks  and  months ;  at  other  times,  they  will  burst 
forth  and  spread  over  certain  parts  of  it  in  great  numbers.  After 
twenty-five  years  of  continued  observations,  M.  Schwabe,  a  German 
astronomer,  discovered  that  there  was  a  periodical  increase  and  de- 
crease of  the  number  and  size  of  the  spots  ;  and  Prof.  Wolf,  of  Zurich, 
by  comparing  the  observations  made  during  the  last  hundred  years, 
has  shown  that  this  period  has  varied  between  8  and  16  years.  These 
periods  are  thought  by  some  to  depend  upon  physical  influences  exerted 
by  some  of  the  planets,  particularly  Venus  and  Jupiter,  when  in  cer- 
tain positions  of  their  orbits. 

Fig.  70. 


m 


SUN-SPOT,   JULY  29,   1860,    STTfttVTN'G  TITR    "  •WTT.T.OW-LE\PM    STRUCTURE. 

b.  The  spots  are  mostly  confined  to  two  zones  parallel  to  the  equator, 
and  extending  from  5°  to  35°  from  it ;  and  they  appear  to  have  a  tend- 
ency to  arrange  themselves  in  lines  parallel  to  the  equator. 

c.  The  duration  of  single  spots  is  also  very  variable.     A  spot  has 
been  seen  to  make  its  appearance   and  vanish  within   twenty-four 


QUESTIONS. -rr.  What  periods  have  heen  established?     b.  To  what  zone  are  the 
spots  mostly  confined  ?    c.  Their  duration  ? 


THE    SUN.  107 

hours  ;  while  others  have  continued  for  nine  or  ten  weeks,  without, 
much  change  of  appearance. 

d.  Their  magnitude  also  presents  very  great  diversity.  Spots  are 
not  unfrequently  seen  that  subtend  an  angle  of  more  than  60",  or 
nearly  seven  times  the  sun's  horizontal  parallax  ;  the  diameter  of  such 
spots  must  therefore  be  more  than  25,000  miles.  A  spot  in  June,  1843, 
continued  visible  to  the  naked  eye  for  a  whole  week,  its  length  being 
estimated  at  74,000  miles.  One  observed  in  1839,  by  Capt.  Davis,  had 
a  linear  extent  of  186,000  miles. 

Fig.  70  represents  a  large  spot  as  seen  and  drawn  by  Mr.  Nasmyth,  an 
English  astronomer,  in  1860.  It  shows  the  umbra,  penumbra,  the  latter 
arching  the  former  as  well  as  surrounding  it,  and  also  the  dotted  or  mottled 
surface  of  the  sun,  as  seen  through  a  powerful  telescope.  The  penumbra 
presents  the  appearances  to  which  Mr.  Nasmyth  has  applied  the  name  of 
44  willow  leaves,"  from  their  fancied  resemblance  to  such  objects. 

155.  THEORIES  AS  TO  THE  PHYSICAL  CONSTITUTION  OF 
THE  SUN.  —  The  most  generally  received  hypothesis  as  to 
the  nature  of  the  sun  is  that  it  is  an  opaque  body  surrounded 
by  an  atmosphere  of  luminous  matter,  and  that  the  spots 
are  openings  in  the  atmosphere,  through  which  the  dark 
body  of  the  sun  becomes  visible. 

a.  This  hypothesis  was  first  advanced  by  Dr.  Wilson,  of  Glasgow, 
in  1769.     In  1793,  Sir  William  Herschel  suggested  the  hypothesis  that 
two  atmospheres  encompass  the  sun  ;  the  first  or  lower  one  being 
formed  of  a  partially  opaque  or  cloudy  stratum  reflecting  light,  but 
emitting  none  of  itself  ;  and  the  second  consisting  of  luminous  mat- 
ter, which  is  the  source  of  the  sun's  light,  and  gives  to  the  disc  its 
form  and  limit.     This  luminous  atmosphere  has  been  sometimes  called 
the  photosphere. 

b.  The  existence  of  a  third  atmosphere,  very  nearly  transparent, 
and  extending  a  great  distance  above  the  photosphere,  is  clearly  indi- 
cated by  the  diminished  brightness  of  the  sun's  disc  toward  the  edges. 

c.  Wilson's  and  Herschel's  hypotheses,  as  developed  and  modified 


.  .  Their  magnitude?  155.  What  generally  received  hypothesis  as  to 
the  cause  of  the  spots  ?  a.  By  whom  advanced  ?  ft.  What  evidence  of  a  third  atmos- 
phere? f.  How  do  Wilson'  8  and  Herschers  hypotheses  explain  the  phenomena? 
Cause  of  the  openings  ? 


108  THE    SUN. 

by  more  recent  observers,  explain  all  the  phenomena  of  the  spots. 
The  black  umbra  is  the  body  of  the  sun,  while  the  penumbra  is  the 
non-luminous  atmosphere,  or  cloudy  stratum,  rendered  visible  by  the 
larger  opening  in  the  photosphere  above  it.  When  this  opening  is 
smaller,  no  penumbra  is  visible ;  and  when  there  is  no  opening  in  the 
cloudy  stratum,  no  black  nucleus  is  visible.  These  openings  or  rents 
are  supposed  by  Sir  John  Herschel  to  be  caused  by  changes  of  tern- 
perature,  in  a  manner  similar  to  the  production  of  tornadoes  and  other 
agitations  of  the  earth's  atmosphere. 

156.  The  spots  and  other  appearances  on  the  sun's  disc 
indicate,  without  doubt,  the  existence  of  a  luminous  atmos- 
phere, consisting  of  gaseous  matter  in  an  incandescent 
state, — like  the  flame  of  an  ordinary  gas-burner, — and 
another  atmosphere,  also  gaseous,  and  almost  perfectly  trans- 
parent, extending  to  a  considerable  distance  beyond. 

a.  The  gasoous  character  of  the  atmosphere,  denied  by  Sir  William 
Herschel,  seems  to  have  been  conclusively  proved  by  M.  Arago,  by  means 
of  an  ingenious  application  of  the  principle  of  polarized  light.   M.  Faye 
estimates  the  height  or  extent  of  the  photosphere  at  4,000  miles. 

b.  KirchhofFs  Hypothesis.— A  simpler  hypothesis  than  Wilson's 
and  HerschePs  has  within  the  last  five  years  been  advanced  by  Kirchhoff, 
a  German  physicist,  and  others,  to  account  for  the  phenomena  of  the 
spots,  consistently  with  the  established  facts,  as  above  stated.    Accord- 
ing to  this  hypothesis  the  nucleus  of  the  sun  is  an  incandescent,  solid 
or  liquid  mass,  the  vapors  arising  from  which  form  the  atmospheres, 
the  denser  and  lower  one  being  luminous  from  the  incandescent  particles 
that  float  in  it.     Changes  of  temperature  in  this  atmosphere  give  rise 
to  tornadoes  and  other  violent  agitations  ;  and  descending  currents  pro- 
duce the  openings,  which  are  dark  because  filled  with  clouds  of  various 
degrees  of  condensation.     This  theory,  and  the  experiments  upon  which 
it  is  based,  are  receiving,  at  present,  much  attention  from  astronomers 
and  physicists  ;  and  there  is  reason  to  believe,  that  when  fully  devel- 
oped, it  will  entirely  supersede  the  cumbrous  and  therefore  improbable 
hypothesis  so  long  and  so  ingeniously  sustained. 


QUESTIONS.— 156.  What  is  certainly  indicated  by  the  phenomena  ?    a.  Gaseous  char- 
acter of  the  atmosphere  ?    b.  Explain  Kirchhoffs  hypothesis. 


THE    SUN. 
Fig.  7L 


109 


£ARTH 

**• 


APPARENT  MAGNITUDES  OF  THE  8TTN. 


157.  The  apparent  diameter  of  the  sun  at  each  of  the 
planets  diminishes  in  proportion  as  the  distance  increases. 
Thus,  at  Mercury,  it  is  2^  times  as  great  as  at  the  earth ; 
but  at  Neptune,  only  ^  as  large. 

a.  The  surface  of  the  solar  disc  at  Mercury  must  therefore  be 
about  6,000  times  as  great  as  at  Neptune,  and  the  intensity  of  its 
light  and  heat  in  the  same  proportion. 

ft.  Various  experiments  seem  to  show  that  the  light  of  the  sun  at 
the  earth  is  equal  to  that  of  600,000  full  moons ;  (Wollaston  estimated 
it  at  800,000.)  The  light  of  the  sun  at  Neptune  must  therefore  be 
equal  to  about  670  times  that  of  the  full  moon  at  the  earth.  The 
electric  light  is  the  only  light  that  approximates  in  intensity  to  the 
light  of  the  sun. 

c.  The  intensity  of  heat  at  the  surface  of  the  sun  has  been  esti- 
mated to  be  300,000  times  that  received  at  any  point  of  the  earth's  sur- 
face. Sir  John  Herschel  supposes  that  it  would  be  sufficient  to  melt  a 
cylinder  of  ice  45  miles  in  diameter,  plunged  into  the  sun,  at  the  rate 
of  200,000  miles  a  second. 

158.  In   addition   to  the  rotation  on  its  axis,  the  sun 
appears  to  have  a  progressive  motion  in  space,  revolving 
with  all  its  attendant  bodies  around  some  remote  star  or 
centre. 

QUESTIONS. — 157.  How  does  the  sun  appear  at  the  different  planets?  a.  Its  surface, 
light,  and  heat,  at  Mercury  and  Neptune?  b.  Light  of  the  sun?  c.  Intensity  of  its 
heat?  15S.  Motion  of  the  sun  and  solar  system  in  space  ? 


110 


ZODIACAL    LIGHT. 


<t.  The  point  to  which  it  is  tending  has,  from  a  vast  number  of 
observations  made  by  different  astronomers,  been  located  in  260°  2(X  oi 
right  ascension,  and  33°  33'  of  declination.  Its  annual  velocity  is  sup- 
posed to  be  about  160  million  of  miles. 

THE  ZODIACAL  LIGHT. 

159.  The  ZODIACAL  LIGHT  is  a  faint  luminous  appear- 
ance, of  the  form  of  a  triangle  or  cone,  seen  at  certain 
seasons  of  the  year,  in  the  evening  at  the  western,  and  in 
the  morning  at  the  eastern  horizon. 

(i.  Its  color  is  a  faint  white,  tinged 
with  yellow  at  the  base,  and  fading 
away  toward  the  apex,  which  is  not 
sharp,  but  obtuse,  or  rounded.  It 
extends  obliquely  from  the  horizon, 
in  the  plane  of  the  sun's  equator, 
and  hence,  very  nearly  in  that  of  the 
ecliptic ;  the  distance  of  its  apex 
from  the  sun  varying  from  40°  to 
100°  or  more.  Its  breadth  at  the 
horizon  also  varies  from  8°  to  30°. 

ft.  It  is  seen  most  distinctly  in 
March  and  April  after  sunset,  and  in 
September  and  October  before  sun- 
rise ;  because,  at  those  times,  the 
ecliptic  is  most  nearly  perpendic- 
ular to  the  horizon.  In  tropical 
regions  it  is  more  conspicuous  than  in  the  higher  latitudes,  and  has 
been  seen  at  midnight  at  both  sides  of  the  horizon  at  once,  extending 
upwards  so  as  almost  to  form  a  luminous  arch. 

It  appeared  thus  to  Chaplain  Jones  of  the  U.  S.  Navy,  who,  from  1853 
to  1857,  made  a  long  and"  careful  series  of  observations  of  it  at  the  equator 
and  between  the  tropics.  He  thought  the  observed  phenomena  proved  it 
to  be  a  nebulous  ring  encompassing  the  earth.  Humboldt,  in  the  same 
latitudes,  also  saw  the  double  appearance  of  this  light. 

QUESTIONS.— «.  To  what  point  is  it  tending?  Its  velocity  ?  159.  What  is  the  zodiacal 
light?  a.  Its  color,  size,  and  direction  of  its  axis ?  6.  When  seen? 


ZODIACAL    LIGHT.  Ill 

c.  Cause  of  the  Zodiacal  Light. — Various  hypotheses  have  been 
suggested  to  account  for  the  zodiacal  light ;  that  most  generally 
received  at  present  is,  that  it  is  a  nebulous  mass  of  great  tenuity, 
of  the  shape  of  a  lens,   encompassing  the  sun  at  its  equator,  and 
extending  sometimes  beyond  the  orbit  of  the  earth. 

d.  It  must  therefore  sometimes  envelop  the  earth  in  the  plane  of  the 
ecliptic ;  and  consequently,  to  a  person  situated  at  the  equator,  or  at 
either  of  the  solstices,  when  the  sun  is  in  the  other,  would  necessarily 
appear,  about  the  time  of  midnight,  at  both  sides  of  the  horizon ;  while, 
farther  north  or  south,  it  would  disappear  at  that  time,  because  viewed 
at  a  lower  altitude,  and  through  its  narrowest  part ;  and  would  there  be 
visible  only  in  the  evening,  near  the  sun,  where  the  line  of  view  would 
penetrate  it  at  its  greatest  thickness. 

€.  Professor  Norton  regards  it  as  made  up  of  "  streams  of  particles 
continually  flowing  away  from  the  sun,  under  the  operation  of  a  force 
of  solar  repulsion  due  to  disturbances  occasioned  by  the  planets  in 
the  magnetic  condition  of  the  particles  composing  the  photosphere, 
and,  therefore,  arising  from  the  same  physical  cause  as  that  which 
produces  the  spots."  He  also  traces  a  connection  between  it  and  the 
luminous  appearance  called  the  corona,  seen  at  the  time  of  a  total 
eclipse  of  the  sun  around  the  obscured  disc.  The  zodiacal  light,  he 
thinks,  "  may  vary  in  brightness  from  one  year  to  another,  with  the 
varying  activity  of  discharge  from  the  sun's  surface."  By  others  it 
has  been  regarded  as  a  vast  ring  of  meteors  circulating  about  the  sun, 
and  finally  impinging  upon  it. 

/.  Meteoric  Theory  of  the  Sun's  Heat.— This  hypothesis  of  a 
constant  shower  of  meteoric  bodies  falling  upon  the  sun,  has  been 
used  to  account  for  the  support  of  its  heat ;  for  their  collision  with  the 
sun  would  necessarily  generate  an  intense  heat,  just  as  iron  may  be 
heated  to  any  degree  by  hammering  it.  It  is  calculated  that  bodies  of 
the  density  of  granite  falling  all  over  the  sun  to  the  depth  of  12  feet 
in  a  year,  and  with  the  velocity  which  they  would  acquire  (384  miles 
in  a  second),  would  maintain  the  solar  heat.  If  Mercury  were  to  strike 
the  sun,  it  would  generate  an  amount  of  heat  equal  to  all  the  sun  emits 
in  seven  years  ;  while  the  shock  of  Jupiter  would  supply  the  loss  of 
more  than  30,000  years. 

QUESTIONS.— c.  How  is  the  zodiacal  light  explained  1    d.  How  is  the  luminous  arch 
explained  f    e.  Professor  Norton's  opinion  ?    /.  Theory  to  account  for  the  sun's  heat  ? 


CHAPTER   IX. 

THE    MOON. 

160.  The  MOON,  although  one  of  the  smallest  bodies  in 
the  solar  system,  is,  to  us,  next  to  the  sun,  the  most  con- 
spicuous, interesting,  and  important,  on  account  of  its  close 
connection  with  our  own  planet,  and  the  effects  which  it 
produces  upon  it. 

161.  The  orbit  of  the  moon  is  elliptical ;  the  point  nearest 
to  the  earth  being  called  the   PEKIGEE,*    and   the  point 
farthest  from  it,  the  APOGEE. f 

162.  Its  mean  distance  from  the  earth  is  238,800  miles ; 
and  it  is  26,000  miles  nearer  to  us  in  perigee  than  in  apogee. 

ft.  Its  eccentricity  is,  therefore,  13,000  miles,  or  about  .055  of  its 
mean  distance.  This  is  more  than  three  times  as  great,  in  proportion, 
as  that  of  the  earth,  which  is  less  than  .017. 

b.  To  Find  its  Distance. — The  distance  of  the  moon  is  found  by 
the  method  and  rule  explained  in  Art.  145.     The  moon's  mean  hori- 
zontal parallax  is  57',  the  sine  of  which  is  .01657 :  hence,  3956  -r-  .01657 
=  238,745  ;  which   is  very  nearly  the  distance  found  by  exact  com- 
putation. 

c.  This  is  the  distance  of  the  moon  from  the  earth's  centre  ;  conse- 
quently it  is  about  4,000  miles  nearer  to  a  point  of  the  earth's  surface 


*  From  the  Greek  words  pert,  meaning  near,  and  gee,  the  earth. 
t  From  the  Greek  words  apo,  meaning  from,  and  gee,  the  earth. 

QUESTIONS.— 160.  What  is  the  moon?  161.  What  is  perigee?  Apogee?  162.  The 
moan  distance  of  the  moon  ?  How  much  greater  in  apogee  than  in  perigee?  a.  The 
eccentricity  of  the  moon's  orbit?  ft.  How  to  calculate  the  distance ?  c.  The  distance 
of  the  moon  at  the  horizon  and  in  the  zenith  ? 


THE    MOON.  113 

directly  under  it ;  and,  with  reference  to  any  particular  place  on  the 
surface  of  the  earth,  its  distance  varies  with  its  altitude,  being  greatest 
at  the  horizon,  and  least  at  the  zenith ;  that  is,  about  4,000  miles 
farther  in  the  horizon  than  when  in  the  zenith. 

Thus  (Fig.  73),  when  the  moon  is  at  A,  in 
the  horizon,  its  distance  from  the  place  P  is 
A  P ;  but  at  B,  in  the  zenith,  it  is  B  P ;  and 
A  P  is  obviously  greater  than  B  P  by 
nearly  the  radius  of  the  earth,  or  about 
4,000  miles. 

d.  Motion  of  the  Apsides. — The  posi- 
tions of  the  apogee  and  perigee  in  space  £ 
are  determined  by  noticing  when  the  moon's  apparent  diameter  is 
greatest  and  when  least.  Careful  observations  of  this  kind  show  that 
these  points  shift  their  positions,  and  that  the  line  of  apsides  completes 
a  circuit  from  west  to  east  in  8?  310id.  This  is  called  the  progression 
of  the  apsides. 

163.  The  inclination  of  the  moon's  orbit  to  the  plane  of 
the  ecliptic  is  about  5 }° ;  consequently,  it  crosses  this  plane 
in  two  points  called  the  moon's  nodes. 

a.  Their  positions  are  ascertained  by  observing  from  day  to  day  the 
distance  of  the  moon's  centre  from  the  ecliptic,  which  is  its  latitude, 
and  noticing  when  the  latitude  becomes  nothing.    It  must  then  be  in 
one  of  the  nodes  ;  when  it  comes  from  the  south,  the  ascending  node, 
and  when  from  the  north,  the  descending  node. 

b.  Motion  of  the  Line  of  Nodes. — The  line  of  nodes,  like  the  line 
of  apsides,  is  subject  to  a  change,  but  in  a  retrograde  direction,  or 
from  east  to  west.    It  completes  a  revolution  in  18^  years. 

164.  The  mean  apparent  diameter  of  the  moon  is  31;]', 
or  a  little  more  than  half  of  a  degree ;   being  about  the 
same  as  that  of  the  sun.     The  real  diameter  of  the  moon  is, 
therefore,  2,162  miles. 

a.  The  Size  of  the  Moon  Calculated. — For  the  distance  multi- 

QUESTIONS.— d.  Motion  of  apsides?  163.  The  inclination  of  the  moon's  orbit? 
Nodes?  a.  How  to  determine  their  positions?  6.  Motion  of  line  of  nodes?  164. 
What  is  the  apparent  diameter  of  the  moon ?  Real  diameter?  «.  How  found  ? 


114  THE     MOON. 

plied  by  the  sine  of  the  apparent  diameter  is  equal  to  the  real  diameter 
(Art.  147,  a).  The  sine  of  the  apparent  diameter  is  .009055,  and 
238,800  X  .009055  =  2162.3,  which  is  the  real  diameter  of  the  moon. 

b.  Surface,  Volume,  Mass. — The  diameter  being  very  nearly  equal 
to  -,3f  that  of  the  earth,  its  surface  is  (-,3, -)2,  or  -,-f  y>  or  about  -fa  of  the 
earth's  surface;  and  its  volume  (ft )3,  or  about  -^  that  of  the  earth. 
Its  mass  is  estimated  to  be  about  -^  of  the  earth's  ;  and  consequently 
its  density  must  be  considerably  less,  about  §•. 

PHASES  OF  THE  MOON. 

165.  The  moon,  when  she  first  becomes  visible  in  the 
west,  is  seen  as   a  slender  crescent ;   but  from  evening  to 
evening  her  form  expands  as  her  angular  distance  eastward 
from  the  sun  increases,  until  when  in  quadrature,  or  90° 
from  the  sun,  half  of  her  disc  is  visible.      When  she  has 
departed  so  far  to  the  east  that  she  rises  just  as  the  sun  sets, 
the  whole  of  her  disc  is  seen,  and  she  is  said  to  be  full. 
After  this   she  becomes  the  waning  moon,  rising  later  and 
later,  and  growing  less  and  less,  until  she  may  be  seen  in 
the  east  as  a  bright  crescent  just  before  sunrise.     A  short 
time  after  this  she  disappears,  and  then   becomes  visible 
again  in  the  west.     These  different  appearances,  called  the 
phases  of  the  moon,  prove  that  she  revolves  around  the  earth 
from  west  to  east. 

166.  When  the  moon   is  in  conjunction,  the  dark  side 
being  turned  toward  us,  she  is  called  new  moon  ;  when  she 
is  in  quadrature  and  shows  half  of  her  disc,  she  is  called 
half-moon;   when    she  is  in  opposition,  she  is  called  full 
moon.    When  she  is  in  quadrature  after  conjunction,  she  is 
said  to  be  in  her  first  quarter ;  when  in  quadrature  after 
opposition,  in  her  last  quarter. 


QUESTIONS. — b.   The   surface,  volume,   and  mass  of  the  moon?     165.    Describe  the 
phases  of  the  moon  ?    166.  What  is  the  phase  in  conjunction,  etc.  ? 


THE    MOOtf. 
Fig.  74. 


115 


PHASES   OP  THR  MOON 


167.  When  she  is  between  conjunction  and  quadrature 
she  assumes  the  crescent  form,  and  is  then  said  to  be  horned  ; 
when  she  is  between  opposition  and  quadrature,  she  exhibits 
more  than  one-half  of  her  disc,  but  not  the  whole,  and  is 
said  to  be  gibbous. 

The  positions  of  new  and  full  moon  are  sometimes  called  the 
tyzygies* 

1C8.  The  phases  of  the  moon  are  the  different  portions  of 
her  illuminated  surface  which  she  presents  to  the  earth  as 
she  revolves  around  it. 


*  From  the  Greek  word  syzygia,  meaning  a  yoking  together. 

QUESTIONS.— 16T.  When  is  the  moon  said  to  be  horned?    Gibbous?     What  are  the 
syzygies?    168.  Define  the  phases. 


V 


116  THE    MOON. 

Fig.  75.  In  Fig.  75,  let  the  par. 

tially  darkened  circle 
represent  the  moon  ;  8^ 
the  direction  of  the  sun ; 
E,  the  direction  of  the 
earth  on  one  side  of  the 
moon,  and  E',  its  direc- 
tion on  the  opposite  side . 
Then  a  6  will  represent 
the  line  which  separates 
the  illuminated  and 
"  £'  darkened  hemispheres  of 

MOON  HOBNKD  AND  GIBBOUS.  the  moon ;  and  c  d,  that 

•which  separates  the  hemisphere  turned  toward  the  earth  from  that  turned 
away  from  it.  At  E,  a  c  being  the  only  part  of  the  disc  visible,  the  moon 
appears  horned  ;  while  at  E',  b  c  being  visible,  the  form  is  gibbous. 

a.  Hence  we  can  find  the  time  of  a  revolution  of  the  moon  by 
observing  the  phases.  If  the  earth  were  at  rest,  the  time  from  one 
new  or  full  moon  to  the  next  would  be  exactly  the  period  of  a  revolution ; 
but  as  the  earth  is  constantly  advancing  in  her  orbit,  when  the  moon 
has  completed  a  revolution,  she  has  to  move  still  farther  in  order  to 
come  into  the  same  relative  position  with  the  earth  and  sun. 

169.  The  time  from  one  new  moon  to  the  next  is  29A 
days.  This  is  the  synodic  period,  and  is  called  a  sy nodical 
month,  or  lunation. 

a.  Sidereal  Period  Calculated.— In  a  year,  or  365 \  days,  the 
moon  makes  365^  -=-  29 -K  or  12 ,4ft  synodic  revolutions  ;  but  the  side- 
real, or  actual,  revolutions  of  the  moon  must  be  one  more  ;  because 
each  synodic  revolution  is  equal  to  one  sidereal  revolution  and  a  part 
of  another,  equal,  in  angular  measurement,  to  the  advance  of  the  earth 
in  her  orbit  during  each  synodic  revolution  of  the  moon.  Hence,  the 
moon  performs  13^  sidereal  revolutions  in  3651  days  :  but  365;  day» 
-^-13,VV:=  27:V  days  (nearly),  which  is,  therefore,  the  time  of  one 
sidereal  revolution. 

In  Fig.  76,  let  A  B  represent  the  advance  of  the  earth  in  its  orbit,  while 
the  moon  completes  a  synodic  revolution,  that  is,  moves  from  c,  the  posi- 
tion of  inferior  conjunction,  till  she  arrives  at  the  same  relative  position 

QUEBTIONR.— a.  What  can  we  find  by  the  phases  ?  169.  What  is  a  synodical  month, 
or  lunation  ?  a.  How  to  find  the  sidereal  period  ?  Explain  by  the  diagram. 


THE    MOON. 


117 


with  the  sun  at  E.     But  when  she  reaches  this  point,  she  has  completed  a 
sidereal  revolution,  and  has  also  moved  from  D  to  E,  a  distance,  it  will  be 

Fisr.  76. 


8IDEEEAL  AND  6TNODICAL  REVOLUTION. 

seen,  equal  in  angular  measurement  to  A  B ;  since  the  arc  A  B  bears  the 
same  proportion  to  the  earth's  orbit  that  E  D  does  to  that  of  the  moon. 

170.  Owing  to  the  constant  advance  of  the  moon  in  her 
orbit,  she  rises  and,  of  course,  arrives  at  the  meridian  and 
sets,  about  50  minutes  later  each  successive  day. 

a.  This  is  the  average  interval  of  time  between  the  successive  ris- 
ings of  the  moon  ;  for  since  she  moves  through  the  ecliptic  in  29£  days, 
her  daily  advance  is  equal  to  about  12i° ;  but  a  place  upon  the  earth's 
surface  moves  15°  in  one  hour,  and  hence,  requires  nearly  50  minutes 
to  overtake  the  moon.  If  the  moon's  orbit  or  the  ecliptic,  since  the 
inclination  is  very  small,  always  made  the  same  angle  with  the  hori- 
zon, this  would  be  the  constant  interval ;  but,  in  consequence  of  the 
obliquity  of  the  ecliptic,  this  angle  continually  varies  during  each 
lunation. 

171.  The  HARVEST  MOON  is  the  full  moon  that  occurs 
in  high  latitudes,  near  the  time  of  the  autumnal  equinox,  in 
September  and  October,  when  she  rises  but  a  little  later  for 
several  successive  evenings,  and  thus  affords  light  for  col- 
lecting the  harvest. 

a.  By  means  of  the  globe,  it  may  be  easily  shown  that  the  ecliptic 
is  most  oblique  to  the  horizon  in  the  signs  Pisces  and  Aries,  and  least 
so  in  Virgo  and  Libra  ;  so  that  when  the  moon  is  in  the  former  signs, 
in  this  latitude,  she  rises  only  about  half  an  hour  later,  but  when  in 

QUESTIONS. — 170.  Why  does  the  moon  rise  later  each  evening?  a.  Why  are  the 
intervals  unequal  ?  171.  What  is  harvest  moon  ?  «.  How  to  explain  this  phenomenon? 


118 


THE    MOON. 


the  latter,  more  than  an  hour.  This  difference  is,  however,  only 
noticed  when  the  moon  happens  to  be  full  while  in  Pisces  or  Aries, 
and  thus  rises,  for  several  evenings,  in  the  higher  latitudes,  but 
a  few  minutes  later.  These  full  moons  must  occur,  of  course,  in 
September  and  October,  when  the  sun  is  in  the  opposite  signs,  Virgo 
and  Libra.  In  the  former  month,  the  full  moon  in  England  is  called 
the  Harvest  Moon  ;  in  the  latter,  sometimes,  the  Hunter's  Moon. 

Let  H  S  H  M  (Fig.  77)  represent 
the  horizon;  S,  the  position  of  the 
sun  at  sunset  ;  M,  the  full  moon 
just  rising ;  SAM,  the  part  of  the 
equator,  and  S  B  M,  the  part  of  the 
ecliptic  above  the  horizon,  the  sun 
being  in  Libra,  the  autumnal  equi- 
nox, and  the  moon  in  Aries,  the 
vernal  equinox.  Since  the  southern 
half  of  the  ecliptic  lies  east  of  Libra, 
it  will  be  evident  that  in  or  near 
this  position  the  ecliptic  must  make 
the  smallest  angle  with  the  horizon ; 
and  consequently,  while  the  moon 
makes  her  daily  advance  in  her 
orbit,  M  6,  she  only  descends  below 
the  horizon  a  distance  equal  to  A  6 ;  while,  if  her  orbit  made  a  greater 
angle  with  the  horizon,  as  S  A  M,  she  would,  by  advancing  through  the 
equal  arc  M  a,  descend  below  the  horizon  a  distance  equal  to  h  a. 

b.  In  the  Polar  Regions,  since  the  full  moon  must  be  opposite  to 
the  sun,  it  remains  constantly  above  the  horizon  ;  and  during  about  15 
days  passes  through  its  changes  without  rising  or  setting,  appearing 
to  move  around  the  horizon ;  and  at  the  pole,  in  a  circle  exactly  parallel 
to  it.    At  the  time  of  the  solstice,  it  is  first  seen  in  the  west  in  its  first 
quarter,  and  continues  constantly  visible  till  the  last  quarter.     These 
brilliant  moonlight  nights  serve  partially  to  compensate  the  inhabit- 
ants of  those  dreary  regions  for  the  long  absence  of  the  sun. 

c.  Moonlight  in  Winter. — The  moonlight  nights  in  the  temperate 
latitudes  are  longer  and  more  brilliant  in  winter  than  in  summer; 
especially  about  the  time  of  the  winter  solstice.    For  when  the  sun  is 
in  Capricorn,  23^°  south  of  the  equinoctial,  the  full  moon  is  in  the  op- 


HARVEBT  MOON. 


QUESTIONS. — 6.  The  moon  as  seen  at  the  polar  regions  ?    c.  Moonlight  in  winter  ? 


THE    MOON.  119 

posite  sign,  Cancer,  23£°  north  of  the  equinoctial,  and  therefore 
culminates  at  a  great  altitude  ;  and,  if  she  happens  to  be  also  at  the 
point  of  her  orbit,  5J7°  north  of  the  ecliptic,  at  her  greatest  altitude, 
which  is  equal  to  the  complement  of  the  latitude  plus  23£°  plus  5|°. 
In  New  York,  this  is  49°  +  23^°  -f  5|°  =  77°  38'. 

172.  Observations  with  the  telescope  show  that  the  moon 
always  presents  very  nearly  the  same  hemisphere  to  the 
earth.  This  proves  that  it  rotates  on  its  axis  once  during 
each  sidereal  month,  or  27 3  days. 

a.  The  unassisted  eye  is  able  easily  to  perceive  that  the  dusky 
spots  on  the  disc  of  the  moon  constantly  keep  in  the  same  relative  po- 
sition and  present  the  same  appearance  ;  and  this  could  not  occur  if 
she  rotated  so  as  to  present  in  succession  different  hemispheres  to  the 
earth.  Just  as  we  infer  a  rotation  of  the  sun  from  the  apparent 
motion  of  the  solar  spots,  so  we  know  that  the  moon  rotates  during 
one  revolution  around  the  earth,  by  the  observed  fact  that  the  lunar 
spots  have  no  apparent  motion ;  since,  if  the  moon  performed  no  rota- 
tion, the  spots  on  its  disc  would  move  across  it  from  west  to  east, 
keeping  pace  with  the  moon's  motion  in  the  ecliptic,  and  completing 
one  apparent  revolution  in  29^  days. 

Fig.  78. 

c     c 


J       \f 


That  the  moon  must  perform  one  rotation  during  each  sidereal  month, 
in  order  to  keep  the  same  side  turned  toward  the  earth,  will  be  evident 
from  the  annexed  diagram  (Fig.  78).  Let  the  line  1,  2,  3,  etc.,  represent 
a  portion  of  the  earth's  orbit,  and  the  dotted  curve  the  real  orbit  of  the  moon, 
as  it  is  carried  by  the  earth  around  the  sun  during  one  lunation.  When 

QUESTIONS.— 172.  How  do  we  know  that  the  moon  rotates  ?    a.  How  to  explain  this? 


120  THE     MOON. 

the  earth  is  at  1,  the  moon  is  full ;  at  2,  last  quarter ;  at  3,  new ;  at  4,  first 
quarter  ;  and  at  5,  full  again.  The  line  a  b  indicates  the  position  of  the 
moon  at  the  commencement  of  a  rotation ;  and  the  parallel  line  c  d,  its 
position  if  it  had  only  completed  a  rotation  at  the  end  of  the  lunation  ;  lout 
it  is  evident  that  in  order  to  keep  the  same  face  to  the  earth  at  5,  it  must 
have  turned  more  than  one  rotation  by  the  angle  contained  between  c  d 
and  ef.  Hence,  during  a  synodic  period,  or  lunation,  the  moon  performs 
more  than  one  rotation,  which  she  completes  in  a  sidereal  period,  or  2?' 
days. 

173.  The  real  orbit  of  the  moon,  as  she  is  carried  by  the 
earth  around  the  sun,  crosses  the  earth's  orbit  every  14.J0, 
but  departs  so  little  from  it  that  it  is  always  concave  to  the 
sun. 

a.  It  will  be  evident  from  Fig.  78,  that  the  moon  crosses  the  earth's 
orbit  twice  during  each  lunation,  or  29^  days  ;  but  there  are  nearly  12^ 
lunations  in  a  year ;  hence  the  moon  must  cross  the  earth's  orbit  25 
times  during  one  year  ;  and  360°  -5-  25  =  14^°  (nearly). 

b.  The  Lunar  Orbit.— The  orbit  of  the  moon,  if  correctly  repre- 
sented in  relation  to  that  of  the  earth,  would  present  the  appearance 
of  a  continuous  curve,  never  crossing  itself,  and  so  slightly  deviating 
from  the  earth's  orbit  as,  unless  drawn  on  a  very  large  scale,  scarcely 
to  be  distinguished  from  it.     This  will  be  evident  when  it  is  considered 
that  the  moon's  distance  from  the  earth  is  only  about  -4- |p0-  of  the  earth's 
distance  from  the  3un.    Why  the  lunar  orbit  is  always  concave  to  the 
sun,  will  be  made  clear  by  the  following  diagram  : — 

Let  the  dotted  curve  ABODE  represent  the  moon's  orbit  crossing1  that 
of  the  earth  at  A,  C,  and  E.  At  A,  the  moon  is  in  first  quarter,  and  west  of 
the  earth  (although  east  of  the  sun) ;  at  B,  it  has  made  one-fourth  of  a  revolu- 
tion, and  is  opposite  to  the  sun  and  full ;  at  C,  it  is  in  last  quarter,  being 
east  of  the  earth ;  at  D,  it  is  new ;  and  at  E,  again  west  of  the  earth  and 
in  first  quarter,  having  thus  completed  one  lunation.  The  arc  A  C  or  C  E 
being  known,  it  it  easy  to  compute  the  distance  of  the  chord  A  C  or  C  E 
from  the  arc.  This  will  be  found  to  be  about  750,000  miles ;  but  as  the 
moon's  distance  from  the  earth  is  only  240,000  miles,  its  orbit  can  never  be 
beyond  the  chord,  but  must,  as  at  C  D  E,  be  within  it ;  and  hence,  must  be 
always  concave  to  the  sun.  In  the  diagram,  the  principle  only  is  illustrated, 


QUESTIONS.— 173.  Describe  the  real  orbit  of  the  moon.    a.  How  often  does  it  cross 
the  earth's  orbit  ?    6.  Why  always  concave  to  the  sun  ?    Explain  from  the  diagram. 


THE    MOON 
Fig.  79. 


the  relative  distance  of  the  moon  being  greatly  exaggerated,  as  well  as  the 
orbital  movement  of  the  earth  during  the  lunation.  The  arc  A  C  E  in  the 
diagram  is  more  than  130°  ,  whereas  it  should  be  only  about  29°. 

c.  Librations  of  the  Moon. — As  the  orbit  of  the  moon  is  elliptical, 
her  velocity  is  not  uniform,  sometimes  exceeding  that  of  her  rotation, 
and  at  other  times  exceeded  by  it.  In  consequence  of  this,  a  small 
portion  of  the  hemisphere  turned  away  from  the  earth  becomes  visi- 
ble alternately  at  the  eastern  and  western  limbs.  This  is  called  the 
libration*  in  longitude.  A  portion  of  her  surface  is  also  exhibited 
alternately  at  each  pole,  caused  by  the  inclination  of  her  axis  to  the 
plane  of  her  orbit.  This  is  called  the  libration  in  latitude. 

The  greatest  extent  of  the  libration  in  longitude  is  7°  53' ;  in  lati- 
tude, 6°  47' ;  and  the  whole  amount  of  the  moon's  surface  made  visible 
by  both  is  about  yfo.  There  is  also  a  third  libration  caused  by  the 
difference  in  the  angle  under  which  the  moon  is  viewed  at  anyplace 
when  on  the  meridian  from  that  at  which  we  see  it  when  at  or  near 
the  horizon.  This  is  called  the  diurnal  libration.  It  is,  however, 
quite  inconsiderable,  amounting  to  only  32"  when  greatest,  and  bring- 
ing into  view  but  T^0  of  the  moon's  surface.  Hence,  -,5(fofio  of  the 
lunar  surface  is  all  that  we  are  ever  able  to  see  ;  -f-g-fc  having  never 
been  gazed  at  by  any  human  eye. 


*  Libration  means  a  balancing,  and  is  applied  in  consequence  of  the  ap- 
parent rolling  or  vibratory  motion  of  the  moon  from  one  side  to  the  other. 


QUESTIONS. — c.  What  are  librations  ?     Of  how  many  kinds  ?    Explain  each, 
much  of  the  moon's  surface  have  we  ever  been  able  to  see  ? 


How 


1.22  THE     MOON. 

d.  Position  of  the  Lunar  Axis. — The  moon's  axis  leans  toward 
its  orbit  6°  39'  ;  hence,  this  is  the  angle  which  the  plane  of  its  equator 
makes  with  that  of  its  orbit ;  and  observation  determines  that  the 
plane  parallel  to  the  ecliptic  lies  between  these  two  planes  /  therefore, 
the  inclination  of  the  moon's  axis  to  the  plane  of  the  ecliptic  is  equal 
to  6°  39'— 5°  8',  (the  inclination  of  the  orbit)  ;  that  is,  1°  31'. 

It  is  a  curious  fact  that  the  line  of  equinoxes  of  the  moon  constantly 
coincides  with  the  line  of  nodes  of  its  orbit,  the  ascending  node  of  its 
orbit  being  situated  at  the  descending  node  of  its  equator.  Hence  the 
lunar  equinoxes  retrograde  with  the  nodes,  and  the  pole  of  the  moon 
revolves  around  that  of  the  ecliptic,  requiring  18?  years  to  complete 
the  circuit. 

Fig-  80.  Fig.  80  represents 

0  the  moon  in  two  po- 
sitions of  her  orbit, 
O  O;  at  1,  in  the 
ascending  node,  and 
at  2,  when  she  has 
her  greatest  north- 
ern latitude.  E  E 
represents  the  plane 
of  the  ecliptic,  and 
E'  E',  a  plane  paral- 
lel to  it,  each  pass- 
ing between  the 
planes  of  the  moon's  equator  and  orbit,  and  at  the  point  where  the  former 
descends  below  the  latter.  The  angular  distance  between  the  planes  E  E 
and  E'  E',  of  course,  never  exceeds  5f  °,  which  is  about  ten  times  the  appar- 
ent diameter  of  the  moon  as  seen  from  the  earth.  Hence,  the  greatest 
distance  between  these  planes  is  about  ten  times  the  diameter  of  the  moon, 
or  21,600  miles,  which  at  the  distance  of  the  sun  subtends  an  angle  of 
about  49",  and  to  this  extent  may  affect  the  inclination  of  the  axis  to  the 
ecliptic. 

174.  Owing  to  the  small  inclination  of  the  moon's  axis 
to  the  plane  of  the  ecliptic  (1°  31'),  she  can  have  but  very 
little  change  of  seasons,  and  that  not  constant,  because  her 
axis  does  not  always  point  in  the  same  direction. 

a.  From  what  has  been  said  above  (Art.  173,  d),  it  will  be  evident 

QUESTIONS. — d.  Explain  and  illustrate  the  position  of  the  lunar  axis.  What  curious 
fact  is  mentioned  ?  174.  What  change  of  seasons  has  the  moon  ?  a.  What  change  »n 
the  equinoxes  and  solstices? 


THE     MOOtf.  123 

that  the  lunar  solstices  and  equinoxes  change  places  with  each  other 
every  9^  years ;  whereas,  the  period  required  for  a  similar  change  in 
the  earth,  occasioned  by  precession,  is  about  13,000  years. 

175.  A  lunar  day  must  be  nearly  15  times  as  long  as  one 
of  our  days,  and  a  lunar  night  of  the  same  length ;  since 
any  place  on  the  moon's  surface  requires  29^  days  to  return 
to  the  same  relative  position  with  the  sun.  Hence  the  sun 
must  remain  above  the  horizon  during  one  half  of  that 
period,  and  below  it  the  other  half. 

a.  Mountains  situated  at  either  of  the  lunar  poles  must  have  per- 
petual day  ;  for  the  sun  there  can  never  be  more  than  \\°  below  the 
horizon  ;  and  on  so  small  a  body  as  the  moon,  the  horizon  would  dip 
that  amount  at  an  elevation  of  about  \  mile. 

b.  The  Earth's  Light. — On  one  hemisphere  of  the  moon,  the  long 
night  must  be  relieved  by  the  light  of  the  earth,  which  exhibits  the 
same  phases  to  the  moon  as  the  latter  does  to  the  earth,  except  that 
they  are  reversed  ;  that  is,  when  the  moon  is  new  to  us,  the  earth  is 
full  to  the  moon  ;  and  when  the  lunar  form  is  but  a  slender  crescent, 
the  earth  is  gibbous,  showing  itself  with  almost  full  splendor.     Now, 
as  the  earth's  disc  contains  about  14  times  as  much  surface  as  that  of 
the  moon,  the  light  of  the  earth  must  cause  a  very  considerable  illu- 
mination. 

c.  The  effect  of  this  is  seen  when  the  moon  is  just  emerging  from 
conjunction,  the  dark  part  of  her  disc  being  slightly  illumined  by  the 
light  of  the  nearly  full  earth,  so  that  the  full,  round  form  of  the 
moon's  disc  becomes  visible,  the  bright  crescent  appearing  at  the  edge 
toward  the  sun.    This  is  sometimes  called  "  the  old  moon  in  the  new 
moon's  arms." 

d.  The   Earth    appears    Stationary  to   the   Moon.— The  earth, 
although  it  exhibits  phases  to  the  moon,  does  not  appear  to  revolve 
around  it,  but  remains  at  every  place  on  the  lunar  hemisphere  which 
is  turned  toward  it,  nearly  at  a  fixed  point  in  the  heavens  ;  this  point 
varying,  of  course,  with  the  change  of  place  of  the  observer.     This 
will  be  obvious,  when  it  is  considered  that  the  rotation  of  the  moon 
would  give  the  earth  an  apparent  motion  from  east  to  west;  but  the 

QUESTIONS.— 1T5.  What  is  the  length  of  a  lunar  day  and  night  ?  a.  Where  is  there 
perpetual  day ?  b.  The  earth's  light— effect  on  the  moon?  c.  "  The  old  moon  in  the 
new  moon's  arms  ?''  d.  Why  must  the  earth  appear  stationary  to  the  moon  ? 


124  THE     MOON. 

motion  of  the  moon  in  her  orbit  would  give  it  an  apparent  motion  at 
the  same  rate,  from  west  to  east ;  hence,  one  counteracts  the  other,  and 
the  earth  appears  to  be  almost  stationary,  only  shifting  its  position 
backward  and  forward  by  the  amount  of  libration. 

176.  Appearances  indicate  that  the  moon  has  very  little, 
if  any,  atmosphere ;   and  that  its  surface  is  as  devoid  of 
water  as  of  air. 

a.  When  viewed  with  a  telescope,  the  surface  of  the  moon  appears 
entirely  unobscured  by  any  clouds  or  vapors  floating  over  it ;  and 
when  the  moon's  edge  comes  in  contact  with  a  star,  the  latter  is  im- 
mediately extinguished ;    whereas,  if  there  were  an  atmosphere,  it 
would,  from  the  effect  of  refraction,  rest  on  the  edge  for  a  short  time ; 
that  is,  it  would  be  visible  when  a  short  distance  actually  behind  the 
moon.    Observations  of  this  kind  have  been  made  with  so  much 
nicety,  that  it  is  believed  that  an  atmosphere  two  thousand  times  less 
dense  than  that  of  the  earth  could  not  have  escaped  detection.     If  any 
atmosphere  therefore  exists,  it  must  be  rarer  than  the  attenuated  air 
in  the  exhausted  receiver  of  the  most  perfect  air-pump. 

b.  The  absence  of  water  follows  from  that  of  air ;  since,  without 
the  latter,  the  heat  of  the  sun  would  be  incapable  of  preserving  the 
temperature  above  the  freezing  point ;  as  we  see  on  the  tops  of  terres- 
trial mountains,  which  are  constantly  covered  with  snow,  from  the 
extreme  rarefaction  of  the  air  at  those  heights.    If  water  existed,  it 
would  therefore  soon  be  converted  into  ice  ;  but  we  see  no  indications 
of  it  even  in  this  form. 

c.  Some  have  accounted  for  this  by  supposing  that  the  internal  heat 
of  the  moon  was  once  very  great,  as  is  that  of  the  earth  at  the  present 
time  ;  but  that  having  cooled,  the  moon  has  contracted  in  volume,  and 
that  vast  caverns  have  thus  been  formed  in  its  interior,  into  which  the 
water  has  penetrated,  and,  of  course,  disappeared.     Indeed,  it  is  obvi- 
ous that  only  great  internal  heat  could  keep  an  ocean  upon  the  surface 
of  a  body  like  the  earth  or  moon. 

SELENOGRAPHY. 

177.  That  part  of  the  moon's  surface  which  is  turned 
toward  the  earth  has  been  very  carefully  observed,  and  all 

QUESTIONS. — 1T6.  Has  the  moon  any  atmosphere  ?    a.  How  is  this  known  ?    6.  Why 
no  water?    c.  How  accounted  for  ?    ITT.  What  is  selenography  ? 


THE    MOON. 


125 


the  objects  upon  it  delineated  upon  maps  or  charts,  so  as  to 
show  their  exact  forms  and  relative  positions.  This  branch 
of  astronomical  science  is  called  SELENOGKAPHY.* 

a,.  This  department  of  the  astronomer's  labors  has  been  prosecuted 
with  extraordinary  zeal  and  industry  by  the  Prussian  astronomers, 
Beer  and  Madler.  Their  chart,  measuring  37  inches  in  diameter, 
exhibits  the  lunar  surface  with  the  most  astonishing  minuteness  and 
accuracy.  Other  charts  have  also  been  constructed  ;  and  the  moon  is 
still  receiving  a  very  scrutinizing  survey  by  a  number  of  eminent 
astronomers,  each  taking  a  separate  belt  or  zone,  with  the  object  of 
arriving  at  still  greater  minuteness  of  delineation. 

178.  The  moon's  disc  when  viewed  through  a  telescope 
presents  a  diversified  appearance  of  dusky  and  bright  spots ; 
the  latter  being  evidently  elevated  portions  of  the  surface, 
and  the  former,  plains  or  valleys. 

u.  The  dusky  patches  were  once  thought  to  be  seas,  and  they  still 
Pig.  81. 


PHOTOGRAPHIC  VIEWS  OF  THE  MOON.—  D«,  L(l  Rue. 

*  From  the  Greek  word  selerie,  the  moon,  and  graphy,  a  description. 


QUESTIONS.—^.  Construction  of  lunar  charts?     ITS.  How  does  the  moon  appeal 
when  viewed  through  a  telescope  ?    «.  What  are  the  dusky  patches  ? 


126 


THE    MOON. 


retain  these  names  in  selenography,  although  without  any  such  literal 
meaning ;  thus,  one  is  called  Mare  Tranquillitatis,  or  Sea  of  Tranquil, 
lity  ;  another,  Mare  Nectaris,  Sea  of  Nectar,  etc. 

b.  Lunar  Mountains. — Mountains  on  the  moon's  surface  are  indi- 
cated by  the  bright  spots  that  appear  scattered  over  the  disc,  and 
beyond  the  terminator,  or  line  that  separates  the  dark  from  the  illumi- 
nated part  of  the  disc,  and  by  the  shadows  cast  upon  the  surface  of  the 
mo3n  when  the  sun  shines  obliquely  upon  these  elevations. 

c.  These  mountains  are  of  various  forms,  including  with  others,  the 
following : — 

1.  Rugged  and  precipitous  ranges,  many  of  a  circular  form,  enclos- 
ing great  plains,  called  on  this  account,  "  Bulwark  Plains,"  from  40  to 

Fig.  82. 


COPERNICUS,  FEOM  A  DBAWING  BY  SIR  JOHN  HEB8CHKL. 

120  miles    in  diameter  ;    2.  Lofty  mountains,  of   a  circular  form, 
enclosing  an  area  from  10  to  60  miles  in  diameter,  resembling  the  crater 

QUESTIONS. — &.  How  are  mountains  indicated  ?      c.  What  classes  of  mountain  for 
mations  ? 


THE    MOON". 


12? 


of  a  volcano  but  of  vast  size,  and  sometimes  containing  in  the  centre  one 
or  more  lofty  peaks :  such  formations  are  called  Ring  Mountains; 
3.  Smaller  cavities,  called  craters,  also  enclosing  a  visible  space,  and  a 
central  mound ;  and  4.  Deep  hollows,  called  holes,  showing  no  enclosed 
area. 

From  the  Ring  Mountains,  streaks  of  light  and  shade  radiate  on  all 
sides,  spreading  to  a  distance  of  several  hundred  miles.  These  are 
called  radiating  streaks.  They  are  attributed  by  some  to  the  streams 
of  lava  which  once  flowed  in  all  directions  from  these  evidently  vol- 
canic mountains. 

(1.  Copernicus. — (Fig.  82) — This  is  one  of  the  grandest  of  the 
Ring  Mountains.  It  is  56  miles  in  diameter,  and  has  a  central 
mountain,  two  of  whose  six  peaks  are  quite  conspicuous.  The 
summit,  a  narrow  ridge,  nearly  circular,  rises  11,000  feet  above  the 
bottom.  It  is  very  brilliant  in  the  full  moon,  sometimes  resembling  a 
string  ot  pearls.  It  lies  on  the  terminator  a  day  or  two  after  first 
quarter.  Another  of  the  Ring  Mountains  (Tycho)  is  visible  to  the 
naked  eye,  in  the  southeast  quadrant  of  the  moon.  It  is  54  miles 
across,  and  is  16,600  feet  high. 

e.  Height  of    Lunar  Mountains.— Beer  and  Madler  have  calcu- 


Fig.  83. 


lated  the  height  of  more  than  1000 
mountains,  several  of  which  reach 
an  elevation  of  23,000  feet,  which 
is  nearly  equal  to  that  of  the  loftiest 
terrestrial  peaks ;  and,  of  course, 
relatively  very  much  greater. 

To  understand  the  principle  on 
which  the  altitude  of  the  lunar  mount- 
ains is  found,  let  E  (Fig.  83)  repre- 
sent the  position  of  the  earth,  C,  the 
centre  of  the  moon,  S,  the  direc- 
tion of  a  ray  of  the  sun,  falling  on  the 
top  of  a  mountain  at  M,  which  there- 
fore appears  to  an  observer  at  E,  at 
the  distance  A  M  from  the  terminator 
at  A.  Now,  this  distance  can  be  found 
by  angular  measurement  and.  calculaT 
tion.  Suppose  it  to  be  about  &  of  the  apparent  diameter  of  the  disc,  or 


QUESTIONS.— d.  Describe  Copernicus,     e.  Height  of  lunar  mountains  ?    How  found  ? 


128  THE    MOOX. 

about  V ;  then  A  M  will  be  &  of  the  moon's  diameter,  or  about  72  miles. 
Then,  from  the  properties  of  the  right-angled  triangle,  (A  C)2  +  (A  M)*  = 
(C  M)2 ;  that  is,  (1080)2  +  (72)*  =  (C  M)«  =  1,171,584 ;  the  square  root  of  which, 
1082.4,  will  be  C  M.  As  this  is  the  sum  of  the  moon's  radius  and  the 
height  of  the  mountain,  the  latter  must  be  1082.4  — 1080  =  2.4  miles. 

/.  The  General  Physical  Condition  of  the  Moon's  Surface, 
therefore,  as  far  as  we  can  observe  it,  is  characterized  by  uniform  deso- 
lation and  sterility.  Sir  John  Herschel  says,  that  among  the  lunar 
mountains  is  seen  in  its  greatest  perfection,  the  true  volcanic  charac- 
ter, as  observed  in  the  crater  of  Mt.  Vesuvius  and  elsewhere,  except 
that  the  internal  depth  of  these  lunar  craters  is  sometimes  two  or 
three  times  as  great  as  the  external  height,  and  that  they  are  of  vastly 
greater  magnitude.  By  means  of  the  great  telescope  of  Lord  Rosse, 
the  interior  of  some  of  these  craters  is  seen  to  be  strewed  with  huge 
blocks,  and  the  exterior  crossed  by  deep  gullies  radiating  from  the 
centre.  No  reliable  indication  of  any  active  volcano  has  ever  been 
obtained  ;  although,  Sir  William  Herschel,  in  1787,  asserted  that  he 
had  seen  three  lunar  volcanoes  in  actual  operation. 

(/.  Are  there  People  in  the  Moon  ? — This  question  has  often  been 
discussed,  but  idly ;  since  no  positive  evidence  can  be  adduced  on  one 
side  or  the  other.  The  distance  of  the  moon  is  too  great  for  us  to 
detect  any  artificial  structures,  as  buildings,  walls,  roads,  etc.,  if  there 
were  any  ;  and  certainly,  without  air  or  water,  no  animals  such  as 
inhabit  our  own  planet  could  exist  there.  But  the  Almighty  Creator 
can  place  animals  and  intelligent  beings  in  any  part  of  the  universe, 
and  accommodate  them  to  the  peculiar  circumstances  of  tlieir  abode  ; 
and  it  would  perhaps  be  strange  if  He  had  left  even  our  little  satel- 
lite without  an  intelligent  witness  of  His  infinite  power  and  benefi- 
cence. 

IRREGULARITIES  OF  THE  MOON'S  MOTIONS. 

179.  The  attraction  of  the  sun  acting  unequally  on  the 
moon  in  different  parts  of  its  orbit  gives  rise  to  very  many 
disturbances  and  irregularities  in  its  motion  ;  so  that  it  is  a 
very  difficult  problem  to  calculate  its  exact  place  at  any 
given  time. 

QUESTIONS.  — /.  Physical  condition  of  the  moon's  surface  ?  g.  Is  the  moon  inhabited  ? 
179.  Lunar  irregularities — how  caused  ? 


THE    MOON.  129 

a.  The  sun's  attracting  force  upon  the  moon  acts  directly  in  con- 
junction  and  opposition,  but,  on  account  of   the  difference  in  the 
distance,  is  greater  in  the  former  position  than  in  the  latter ;  while  at 
the  quadratures,  it  acts  obliquely,  thus  giving  rise  to  a  variety  of  dis- 
turbances, or  perturbations. 

b.  The  attraction  of  the  sun  upon  the  moon  is  absolutely  more  than 
twice  as  great  as  that  of  the  earth ;    but  being  very  nearly  equal 
on  both  earth  and   moon,   they  move  with  regard  to  each  other 
almost  as  if  they  were  not  attracted  at  all  by  the  sun.    If  the  attrac- 
tion of  the  sun  upon  the  earth  were  suspended,  the  moon  would 
abandon  the  earth,  and  either  revolve  around  the  sun,  or  move  directly 
to  it.    As  the  distance  of  the  earth  and  moon  from  each  other  is  so 
small  relatively  to  their  distance  from  the  sun  (about  -3-i4-),  their  mutual 
attractions  are  not  much  disturbed  by  the  action  of  the  sun ;  but  they 
are  to  some  extent.    Thus,  in  conjunction,  the  moon  is  attracted  more 
than  the  earth,  but  in  opposition,  less ;  so  that  the  tendency  of  the 
sun's  force  is  to  pull  them  apart  when  in  either  of  these  positions.    In 
the  quadratures,  however,  the   sun's  force  acts  obliquely,  and  con- 
sequently tends  to  pull  them  together.      Hence,  we  may  say,  the 
attraction  of  the  earth  upon  the  moon  is  diminished  in  the  syzygies, 
and  increased  in  the  quadratures. 

c.  The  following  are  the  principal  irregularities  or  inequalities  to 
which  the  moon's  motion  is  subject :  (Those  completed  in  short  periods 
are  called  periodical;  those  that  require  very  long  periods  for  their 
completion  are  called  secular) 

1.  Ejection,  which  is  the  largest  of  these  inequalities,  is  the  variation 
in  the  moon's  longitude,  due  to  the  action  of  the  sun,  above  referred  to. 
It  depends  upon  the  moon's  angular  distance  from  the  sun,  and  the 
eccentricity  of  its  orbit.    By  it  the  equation  of  the  centre  of  the  moon 
is  diminished  in  syzygies  and  increased  in  quadratures.     It  may  influ- 
ence the  moon's  longitude  to  the  extent  of  1°  SO*.    This  irregularity 
was  discovered  by  Ptolemy. 

2.  The  variation,  which  also  affects  the  longitude  of  the  moon  to 
the  extent  of  3(X.     It  arises  from  the  disturbing  force  of  the  sun,  act- 
ing upon  the  moon  when  in  the  octants,  or  points  half-way  between 
the  syzygies  and  quadratures.     This  was  discovered  by  Tycho  Brahe, 

QUESTIONS. — a.  How  does  the  sun's  force  act?    b.  Its  effect  in  syzygies  and  quadra- 
tures?   c.  What  is  evection  ?    The  variation  ? 


130  THE    MOON. 

and  was  the  first  lunar  inequality  explained  by  Sir  Isaac  Newton  by 
applying  the  law  of  gravitation. 

3.  The  annual  equation,  which  results  from  the  varying  velocity  of 
the  earth  in  its  orbit.     It  may  affect  the  moon's  longitude  about  11'. 

4.  The  parallactic  inequality,  arising  from  variations  in  the  disturb- 
ing force  of  the  sun  upon  the  moon  according  as  the  latter  is  in  that 
part  of  its  orbit  nearest  to,  or  farthest  from,  the  sun.    It  may  affect  the 
moon's  longitude  to  the  extent  of  2'. 

5.  The  secular  acceleration  of  the  moon's  mean  motion,  caused  by 
the  diminution  of  the  eccentricity  of  the  earth's  orbit.     At  present  it 
amounts  to  10"  every  100  years,  the  periodic  time  of  the  moon  being 
constantly  diminished  to  that  extent.    This  was  discovered  by  Halley 
in  1693,  by  comparing  the  periodic  time  of  the  moon,  as  deduced  from 
Chaldean  observations  of  eclipses  made  at  Babylon,  720  and  719  B.C., 
with  Arabian  observations  made  in  the  8th  and  9th  centuries  A.D. 
La  Place  demonstrated  its  cause.     At  a  very  distant  period,  this 
inequality  will,  of  course,  be  reversed,  becoming  a  retardation  instead 
of  an  acceleration. 

d.  Other  irregularities  have  been  discovered,  caused  by  the  disturb- 
ing action  of  Venus.  These  various  inequalities  constitute  what  is 
called  the  Lunar  Theory  ;  and  when  they  are  all  applied,  the  computed 
place  of  the  moon  should  precisely  agree  with  the  observed  place. 

QUESTIONS.— The  annual  equation  ?  The  parallactic  inequality  ?  The  secular  accele- 
ration ?  d.  What  other  inequalities  ?  The  Lunar  Theory  ? 


CHAPTER    X. 


ECLIPSES. 

180.  An  ECLIPSE  *  is  the  concealment  or  obscuration  of 
the  disc  of  the  sun  or  moon  by  an  interception  of  the  sun's 
rays.    Eclipses  are,  therefore,  either  Solar  or  Lunar. 

181.  A  SOLAR  ECLIPSE  is  caused  by  the  passage  of  the 
moon  between  the  earth  and  sun  so  as  to  conceal  the  sun 
from  our  view. 

182.  A  LUNAR  ECLIPSE  is  caused  by  the  passage  of  the 
moon  through  the  earth's  shadow. 

a.  By  a  shadow  is  meant  simply  the  space  from  which  the  light  of  a 
luminous  body  is  wholly  intercepted  by  the  interposition  of  some 
opaque  body.  Since  light  proceeds  from  a  luminous  body  in  straight 
lines,  and  in  all  directions,  the  darkened  space  formed  behind  the 
earth  or  moon  must  be  conical ;  that  is,  of  the  form  of  a  cone,  circular 
at  the  base  and  terminating  at  a  point ;  since  the  sun  or  luminous 
body  is  larger  than  either  of  the  opaque  bodies.  The  shadow  is  some- 
times called  by  its  Latin  name,  umbra. 

b»  Besides  the  totally  darkened  space  called  the  umbra,  there  is 
formed  on  each  side  a  space  from  which  the  light  is  only  partially 
excluded ;  this  is  called  the  penumbra.^  The  relations  of  the  umbra 

*  From  the  Greek  word  ekleipsis,  which  means  a,  fainting  away.  The  ecliptic 
is  so  called  because  eclipses  only  take  place  when  the  moon  is  in  its  plane. 

t  From  the  Latin  word  pene,  meaning  almost,  and  umbra,  meaning  a 
shadow. 

QUESTIONS.— 180.  What  is  an  eclipse?  Of  how  many  kinds?  .181.  How  is  a  solar 
eclipse  caused?  182.  A  lunar  eclipse?  a.  How  is  a  shadow  defined?  The  form  oi 
the  earth's  or  moon's  shadow  ?  ft.  Define  the  terms  umbra  and  penumbra. 


132  ECLIPSES. 

to  the  penumbra  will  be  understood  by  inspecting  the  annexed  dia- 
gram (Fig.  84). 

Pig.  84. 


80LAB  AND   LUNAB   ECLIPSES. 

183.  If  the  moon  moved  exactly  in  the  plane  of  the 
earth's  orbit,  a  solar  eclipse  would  occur  at  every  new  moon, 
and  a  lunar  eclipse  at  every  full  moon ;  but  as  the  moon's 
orbit  is  inclined  to  that  of  the  earth,  an  eclipse  can  only 
happen  when  the  moon  is  at  or  near  one  of  its  nodes. 

a.  When  the  moon  is  new  or  full  at  a  considerable  distance  from 
its  node,  it  is  too  far  above  or  too  far  below  the  plane  of  the  ecliptic  to 
intercept  the  sun's  rays  from  the  earth,  or  to  pass  within  the  limits  of 
the  earth's  shadow.  It  will  be  easily  understood  that  no  eclipse  can 
occur  unless  the  sun,  earth,  and  moon  are  situated  exactly  or  nearly 
in  the  same  straight  line.  [See  Fig.  84.] 

ft.  The  limit  north  or  south  of  the  ecliptic  within  which  an  eclipse 
must  occur  is  larger  in  the  case  of  solar  than  in  the  case  of  lunar 
eclipses.  In  the  former  it  varies  from  1°  35'  to  1°  24' ;  in  the  latter, 
from  63'  to  52'. 

QUESTIONS. — 183.  Where  must  the  moou  be  when  an  eclipse  occurs  ?  «.  How  sx- 
plained?  b.  What  is  the  limit  in  latitude  for  solar  and  lunar  eclipses  ?  Explain  and 
demonstrate  each  by  Fig.  85. 


ECLIPSES  133 

Fig.  85. 


To  explain  how  this  is  found,  let  S  be  the  centre  of  the  sun,  and  O  the 
centre  of  the  earth,  S  O  E  being  the  plane  of  the  ecliptic ;  let  also  P  be 
the  position  of  the  moon  at  the  limit  for  a  solar  eclipse,  and  V,  its  position 
for  a  lunar  eclipse.  The  angular  distance  of  the  moon's  centre  from  the 
ecliptic  in  each  case  is  the  limit  required;  S  O  m  is  that  angle  for  the  for- 
mer, and  n  O  E,  for  the  latter.  Now,  S  O  m  is  equal  toSOB  +  POm  + 
B  O  P ;  and  S  O  B  is  the  apparent  semi-diameter  of  the  sun,  and  P  O  m  is 
that  of  the  moon.  But,  O  P  C,  being  exterior  to  the  triangle  B  O  P,  is 
equal  to  the  sum  of  the  two  interior  angles  O  B  P  and  BOP,  and  hence 
B  O  P  is  equal  to  O  P  C  —  O  B  C,  or  the  moon's  horizontal  parallax 
minus  that  of  the  sun.  Therefore,  the  solar  limit  in  latitude  is  equal  to  the 
sum  of  the  apparent  semi-diameters  of  the  sun  and  moon  increased  by  the  differ- 
ence between  the  horizontal  parallax  of  each  ;  or  16i'  +  161' -f  1°  2'  =  1°  35',  when 
greatest  (omitting  the  sun's  parallax,  which  is  very  small) ;  and  15J'  +  14V 
+  535'  -  1°  24',  when  least.  Hence,  when  the  moon's  latitude  at  the  time 
of  inferior  conjunction  does  not  exceed  the  former,  an  eclipse  may  occur; 
when  it  does  not  exceed  the  latter,  an  eclipse  must  occur. 

The  angle  of  limit  for  a  lunar  eclipse  is  n  O  E,  obviously  less  than  S  Om. 
It  is  composed  of  the  angle  n  O  V,  or  the  apparent  semi-diameter  of  the 
moon,  and  the  angle  V  O  E,  or  the  angle  subtended  by  one-half  of  the 
diameter  of  the  shadow,  where  the  moon  traverses  it.  Now,  V  O  E  =  O  V  D 
-OEV,  and  OEV=AOS-OAD;  hence  VOE  =  OVD  +  OAD 
—  A  O  S.  But  0  V  D  is  the  moon's  horizontal  parallax,  O  A  D  is  that  of 
the  sun,  and  A  O  S  is  the  sun's  apparent  semi-diameter.  Consequently, 
n  O  E,  or  the  lunar  limit  in  latitude,  is  equal  to  the  sum  of  the  horizontal 
parallax  of  the  sun  and  moon,  diminished  by  the  sun's  apparent  semi-diameter, 
and  increased  by  that  of  the  moon.  That  is,  62'  —  15J'  + 161'  =  63',  when 
greatest ;  and  53^  —  16^+14^  =  52',  when  least.  These  calculations,  being 
made  only  for  illustration,  are  but  approximatively  correct. 

184.  The  distance  in  longitude,  either  side  of  the  node, 

QUESTION.— 184.  What  is  meant  by  the  ecliptic  limit? 


134 


ECLIPSES. 


within  which  an  eclipse  can  occur,  is  called  the  ECLIPTIC 
LIMIT. 

185.  The  solar  ecliptic  limit  extends  about  17°  on  each 
side  of  the  node ;  the  lunar  ecliptic  limit,  about  12°. 

a.  This  difference  follows  from  the  difference  in  the  limits  in  lati- 
tude, the  ecliptic  limits  in  longitude  being  computed  from  those  in 
latitude. 

Fig.  86.  For  in  Fig.  86,  let  B  N  be 

a  portion  of  the  ecliptic, 
A  N,  a  part  of  the  moon's 
orbit,  N,  the  node,  A  B,  the 


solar  limit  in  latitude  and 
C  D,  the  lunar.  It  will  be 
at  once  apparent  that  since 
A  B  is  greater  than  C  D,  it 
must  be  farther  from  the  node.  To  calculate  the  exact  amount,  there  are 
given,  in  the  right-angled  triangle  A  N  B,  the  angle  at  N  =  5}° ;  the  side 
A  B  or  C  D,  and  the  right  angle  at  B,  to  find  the  side  B  N  or  D  N,  which 
can  easily  be  done  by  the  higher  mathematics. 

b.  Since  the  limits  in  latitude  vary,  those  in  longitude  also  vary, 
the  amount  given  above  being  the  mean.  The  greatest  solar  ecliptic 
limit  is  18°  36' ;  and  the  least,  15°  2(X  ;  the  greatest  lunar  ecliptic  limit 
is  12°  24' ;  and  the  least,  9°  23'.  Within  the  former,  an  eclipse  may 
happen  ;  within  the  latter,  it  must. 

Fig.  87. 


*    * 


m  $ 


PATH    OF  THE   STTN   OBO88ED    BY   THAT    OK   THE  MOON. 

Fig.  87  illustrates  the  relative  position  of  the  sun  and  moon's  orbits, 
with  respect  to  the  ecliptic  limits.  In  the  centre  the  moon  is  exactly  at  the 
ascending  node;  while  at  the  extremes,  it  is  at  the  limits  both  in  latitude 
and  longitude.  Except  at  the  node,  the  moon,  it  will  be  apparent,  only 
partially  covers  the  disc  of  the  sun,  within  the  limits  on  each  side. 

QUESTIONS.— 185.  What  is  the  extent  of  the  solar  and  lunar  ecliptic  limits  f  a.  Why 
do  they  differ  ?  b.  Why  is  each  not  always  the  same  ? 


ECLIPSES.  135 

186.  Since  the  solar  ecliptic  limits  are  wider  than  the 
lunar,  eclipses  of  the  sun  are  more  frequent  than  those  of 
the  moon. 

187.  The  greatest  number  of  eclipses  that  can  happen  in 
a  year  is  seven ;  five  of  the  sun  and  two  of  the  moon,  or  four 
of  the  sun  and  three  of  the  moon.    The  least  number  is 
two,  both  of  which  must  be  of  the  sun. 

a.  The  usual  number  is  four,  and  it  is  rare  to  have  more  than  six. 
From  the  above  statement,  it  will  be  seen  that  the  greatest  number  of 
solar  eclipses  is  five,  and  the  least  two  ;  and  that  the  greatest  number 
of  lunar  eclipses  is  three,  while  none  at  all  may  occur  during  the  year. 

b»  Number  of  Solar  Eclipses. — Since  the  sun  crosses  the  line  of 
nodes  twice  each  year,  and  his  monthly  progress  in  the  ecliptic  is  about 
29°,  while  a  solar  eclipse  must  occur  if  the  moon  is  within  15°  20'  of 
either  node,  or  within  a  space  of  30°  407,  there  must  evidently  be  a 
solar  eclipse  each  time  the  sun  passes  the  node,  or  twice  each  year. 
Now,  if  the  sun,  at  the  time  of  new  moon  is  18°  west  of  the  node,  it 
may  be  eclipsed  (Art.  185,  6) ;  and  if  it  were,  there  would  be  another 
eclipse  at  the  next  new  moon,  for  the  sun  would  have  advanced  less 
than  11°  east  of  the  node.  Again,  in  six  lunations  from  the  first  new 
moon  referred  to,  the  sun  would  have  advanced  174°,  and  consequently 
would  be  174°— 18°,  or  156°  east  of  one  node,  and  24°  west  of  the 
other ;  but  the  node  is  itself  moving  to  the  west  about  1£°  every  luna- 
tion ;  and  hence,  the  sun  would  be  only  24° — 9°,  or  15°,  from  the 
node,  so  that  a  third  eclipse  would  take  place ;  and  after  another 
lunation,  a  fourth,  since  the  sun  would  then  be  less  than  15°  from  the 
node.  Now,  owing  to  the  retrogradation  of  the  nodes,  the  sun  passes 
from  one  to  the  same  again  in  346  days  ;  and  hence,  if  it  passed  one  at 
the  beginning  of  the  year,  it  would  pass  it  again  toward  the  end  of 
the  year,  and  there  would  be  three  passages  of  a  node  in  that  time  ; 
so  that  if  four  eclipses  had  previously  taken  place,  there  might  be  still 
another  toward  the  end  of  the  year,  making  Jive  in  all. 

c.  Number  of  Lunar  Eclipses. — As  the  space  on  each  side  of  the 
node,  within  which  a  lunar  eclipse  must  occur,  is  only  about  9£°,  or  19° 


QUESTIONS.— 186.  What  eclipses  are  more  frequent?  Why?  1ST.  What  is  the 
greatest  number  of  eclipses  in  a  year?  The  least?  «.  The  usual  number?  How 
many  solar  eclipses  may  happen  ?  Lunar  eclipses  ?  ft.  How  is  this  proved  in  respect 
to  solar  eclipses  ?  c.  Lunar  eclipses  ? 


136  ECLIPSES. 

on  both  sides,  it  is  obvious  that  there  might  be  no  lunar  eclipse  during 
the  year ;  but,  since  an  eclipse  may  occur  within  a  space  of  25°  (12°  24 
on  each  side  of  the  node),  it  follows  that  one  lunar  eclipse  may  occur 
at  each  passage  of  the  sun,  or  three  during  the  year.  But  three  lunar 
eclipses  can  not  be  preceded  by  five  solar  eclipses  in  the  same  year ;  for 
two  solar  eclipses  can  not  take  place  at  each  node,  unless,  at  the  first  one, 
the  sun  is  at  least  about  15°  west  of  the  node,  so  that  there  would  not 
be  enough  space  at  the  end  of  the  year  for  both  a  solar  and  a  lunar 
eclipse. 

188.  Solar  eclipses  do  not  actually  occur  as  often  as  lunar 
eclipses  at  any  particular  place  ;  because  the  latter  are  always 
visible  to  an  entire  hemisphere,  whereas  the  former  are  only 
visible  to  that  part  of  the  earth's  surface  covered  by  the 
moon's  shadow  or  its  penumbra, 

a.  That  the  moon,  in  a  lunar  eclipse,  is  concealed  from  an  entire 
hemisphere,  will  be  obvious  from  the  fact  that  the  diameter  of  the 
earth's  shadow  where  the  moon  crosses  it  is  always  more  than  twice  as 
great  as  the  diameter  of  the  moon,  and  is  sometimes  nearly  three  times 
as  great.  For  the  angle  VOW  (Fig.  85)  is  equal  to  the  sum  of  the  hori 
zontal  parallax  of  the  sun  and  moon,  diminished  by  the  apparent  semi 
diameter  of  the  sun  (183,  b).  The  greatest  parallax  of  the  moon  is  about 
62',  and  the  least,  53 \' ;  and  the  least  apparent  semi-diameter  of  the 
the  sun  is  152',  and  the  greatest,  16V  >  hence,  the  angle  V  0  W  is, 
when  greatest,  44  V  (omitting  the  sun's  parallax) ;  and  when  least,  37V  J 
the  mean  being  about  40!|'.     As  this  is  the  angular  value  of  the  semi- 
diameter  of  the  shadow,  it  must  be  doubled  for  the  whole,  which 
therefore  is,  when  greatest,  88^' ;  least,  74^' ;    mean,  81|'.      Hence, 
as  the  moon's  apparent  diameter  is,  when  greatest,  33£' ;  least,  29^' ; 
mean,  31?',  the  truth  of  the  above  statement  will  be  apparent. 

b.  Length  of  the  Earth's  Shadow. — This  can  be  readily  found  by 
comparing  the  triangles  A  S  E  and  DEO  (Fig.  85),  which  being  both 
right-angled    triangles,    and    having    all    their   angles   respectively 
equal,  have,  by  a  principle  of  geometry,  proportional  sides ;  so  that 
AS:DO::SE:OE.     But  D  0,  the  semi-diameter  of  the  earth,  is  about 
Ttnr  °f  -A.S,  the  semi-diameter  of  the  sun;  hence  OE,  the  length  of 

QUESTIONS.— 188.  What  eclipses  are  the  more  frequent  at  any  place  ?  Why  ?  «. 
Why  is  the  moon  concealed  from  an  entire  hemisphere  ?  6.  What  is  the  length  of  the 
earth's  shadow  ?  How  demonstrated  ? 


ECLIPSES. 


137 


th«  shadow,  must  be  To--7  of  S  E  ;  and  therefore,  S  0  must  be  |£f  of  the 
whole  distance  S  E,  and,  of  course,  SE,  \$l  of  SO;  but  OE,  the 
length  of  the  shadow,  is  equal  to  S  E—  S  O ;  hence  it  is  equal  to  -fa  of 
S  0,  or  the  distance  of  the  earth  from  the  sun.  Therefore  its  greatest 
length  is  about  877,000  miles,  and  its  least,  850,000  miles ;  that  is,  at 
its  mean  length,  a  little  more  than  the  diameter  of  the  sun. 

Fig.  88. 


c.  Length  of  the  Moon's  Shadow. — This  can  be  found  by  a  similar 
calculation.  Let  S  (Fig.  88)  be  the  centre  of  the  sun,  and  O,  that  of  the 
moon  ;  P  will  then  be  the  end  of  the  shadow,  and  0  P  its  length ;  and, 
inthetrianglesASPandOMP,AS:MO::SP:OP.  Now,  MO  is 
about  TJ£T  of  A  S  ;  hence  O  P  is  y^  of  S  P,  and  S  0,  \\\  of  S  P ;  or  S  P, 
\\\  of  S  O ;  therefore  O  P  is  -3^  of  S  0,  the  distance  of  the  moon  from  the 
sun.  Now,  the  moon's  distance  from  the  earth  varies  between  252,000 
miles  and  226,000  miles ;  and  the  earth's  distance  from  the  sun, 
between  93  millions  and  90  millions ;  hence,  at  the  mean  distance  of 
the  earth  and  moon,  the  length  of  the  shadow  is  about  232,000  miles, 
or  6,000  miles  from  the  earth's  centre,  and  2,000  miles  from  its  surface. 
When  the  earth  is  in  aphelion  and  the  moon  in  perigee,  it  extends 
about  10,000  miles  beyond  the  earth's  centre,  or  14,000  miles  from  the 
surface  a  b,  which  is  the  maximum.  When  the  earth  is  in  perihelion 
and  the  moon  in  apogee,  the  shadow  is  about  228,000  miles  long, 
while  the  moon  is  252,000  miles  from  the  earth's  centre ;  so  that  it 
fails  to  reach  the  surface  of  the  earth  by  20,000  miles. 

fl.  Breadth  of  the  Moon's  Shadow. — When  the  end  of  the 
shadow  extends  to  the  greatest  distance  beyond  the  earth's  centre,  the 
amount  of  surface  covered  by  it  is  the  greatest  possible.  Let  a  b  (Fig. 
88)  be  the  diameter  of  the  shadow  where  it  intersects  the  earth  ;  and 

QUESTIONS.— c.  The  length  of  the  moon's  shadow?  How  demonstrated  ?  d.  How 
much  of  the  earth's  surface  may  he  obscured  by  the  moon's  shadow  ?  How  proved  ? 
How  much  by  the  moon's  penumbra  ? 


138  ECLIPSES. 

since  it  is  a  very  small  arc,  we  may  find  its  approximate  length  by  con- 
sidering it  a  straight  line.  We  shall  then  have,  by  comparing  the 
triangles,  A  P  :  a  P  : :  A  S :  %a  b  ;  but  a  P  is  14,000  miles  (183  c),  and  A  P  is 
93,014,000  miles.  Hence,  93,014,000  : 14,000 : :  426,000  :  \a  b  =64  miles+. 
Therefore  a  6,  or  the  breadth  of  the  shadow  where  it  intersects  the 
earth  is  about  128  miles.  The  breadth  of  the  portion  of  the  earth's 
surface  covered  by  the  shadow  is,  really,  1°  54',  or  130  miles.  This  is  the 
maximum.  The  breadth  of  the  greatest  portion  of  the  earth's  surface 
ever  covered  by  the  moon's  penumbra  is  70°  17',  or  4,850  miles. 

189.  When  the  whole  of  the  sun's  or  moon's  disc  is  con- 
cealed, the  eclipse  is  said  to  be  total ;  when  only  a  part  of 
it  is  concealed,  it  is  said  to  be  partial. 

190.  In  order  to  measure  the  extent  of  the  eclipse,  the 
apparent  diameters  of  the  sun  and  moon  are  divided  into 
twelve  equal  parts,  called  digits. 

Fig.  89. 


A  PARTIAL  ECLIPSE  OF  THE  BUN  AND  MOON. 

a.  The  conditions  of  a  total  and  a  partial  eclipse  will  be  apparent 
from  the  explanations  already  given.  When  the  centres  of  the  sun 
and  moon  coincide,  that  is,  when  the  latter  is  exactly  at  the  node,  the 
eclipse  is  said  to  be  central.  A  central  eclipse  of  the  moon  must,  of 
course,  be  total ;  but  a  solar  eclipse  may  be  central  without  being 
total ;  since  sometimes,  as  it  has  been  demonstrated,  the  shadow  of  the 
moon  does  not  reach  the  earth.  The  moon,  when  this  is  the  case,  covers 


QUESTIONS.— 189.  When  is  an   eclipse  total?    When  partial  ?    190.  What  are  digits  1 
a.  What  is  a  central  eclipse  ? 


ECLIPSES.  139 

only  the  central  part  of  the  sun's  disc,  leaving  a  ring  of  luminous  sur- 
face visible  around  the  opaque  body.     This  is  called  an  annular  * 

eclipse. 

191.  An  ANNULAR  ECLIPSE  is  an  eclipse  of  the  sun,  which 
happens  when  the  moon  is  too  far  from  the  earth  to  conceal 
the  whole  of  the  sun's  disc,  leaving  a  bright  ring  around  the 
dark  body  of  the  moon. 

192.  The  time  at  which  an  eclipse  will  occur  may  be  dis- 
covered by  finding  the  mean  longitudes  of  the  sun  and  node 
at  each  new  or  full  moon  throughout  the  year,  and  compar- 
ing the  difference  of  the  longitudes  with  the  ecliptic  limits. 

Fig.  00. 


AN  ANNULAR  ECLIP8R. 

a.  Cycle  of  Eclipses. — Eclipses  of  both  the  sun  and  moon  recur 
in  nearly  the  same  order,  and  at  the  same  intervals,  after  the  expiration 
of  18  years  and  10  or  11  days  (according  as  there  may  be  5  or  4  leap- 
years  in  this  period).  For  a  lunation  is  about  29.53  days,  and  the  time 
of  a  revolution  of  the  sun  with  respect  to  the  node,  346.62  days,  which 
periods  are  nearly  in  the  ratio  of  19  to  223  ;  so  that  223  lunations  are 
almost  equal  to  19  revolutions  of  the  sun  ;  and  346.62  days  X  19=  18* 
llf,d .  This  is  called  the  cycle  or  period  of  eclipses.  The  eclipses  which 
occur  during  one  such  period  being:  noted,  subsequent  eclipses  may 
easily  be  predicted  ;  as  their  order  is  the  same,  only  they  are  10  or  11 
days  later  in  the  month,  and  about  eight  hours  later  in  the  day ;  so 


*  From  the  Latin  word  annulus,  meaning  a  ring. 


QUFBTIONR  —  191.  What  is  an  annular  eclipse ?  How  caused?  192.  How  to  predict  an 
eclipse  ?  a.  What  is  the  cycle  of  eclipses  ?  How  calculated  ?  How  named  by  the  Chaldeans  ? 


140  ECLIPSES. 

that  in  one  cycle  eclipses  may  be  visible,  and  in  the  next  invisible,  to  a 
particular  place.  During  this  period  there  are  generally  41  solar  and 
29  lunar  eclipses.  This  cycle  was  known  to  the  ancient  Egyptians 
and  Chaldeans,  and  called  by  them  Saros. 

193.  The  phenomena  connected  with  a  total  eclipse  of  the 
sun  are  of  a  peculiarly  interesting  character,  and  have  been 
observed  by  astronomers  with  great  attention  and  industry. 

a.  To  an  ignorant  mind,  this  occurrence  must  be  the  occasion  of 
very  great  awe,  if  not  actual  terror.  A  universal  gloom  overspreads 
the  face  of  the  earth  as  the  great  luminary  of  day  appears  to  be  ex- 
piring in  the  sky  ;  the  stars  and  planets  become  visible,  and  the  animal 
creation  give  signs  of  terror  at  the  dismal  and  alarming  aspect  of 
nature.  Armies  about  to  engage  in  battle  have  thrown  down  their 
arms  and  fled  in  dismay  froin  the  seeming  angor  of  heaven.  This  was 
the  case  at  the  eclipse  predicted  by  Thales,  which  occurred  on  the  eve 
of  the  battle  between  the  Medes  and  Lydians,  584  B.C. 

ft.  Phenomena  of  a  Solar  Eclipse,— The  following  are  the  most 
interesting  of  the  phenomena  presented  Curing  a  total  eclipse  of  the 
sun : — 

1.  The  change  of  color  in  the  sky  from  its  ordinary  blue  or  azure 
tinge  to  a  dusky,  livid  color  intermixed  with  purple.     Kepler  men- 
tions that  during  the  solar  eclipse  in  1590,  the  reapers  in  Styria  noticed 
that  every  thing  had  a  yellowish  tinge.   The  darkness  is  not,  however, 
total,  but  sufficiently  great  to  prevent  persons'  reading. 

2.  The  corona,  or  halo  of  light  which  appears  to  surround  the  moon 
while  it  covers  the  disc  of  the  sun.     This  is,  at  the  present  time,  sup- 
posed to  be  caused  by  the  atmosphere  of  the  sun. 

3.  When  the  moon  has  almost  covered  the  disc  of  the  sun,  leaving 
only  a  line  of  light  at  the  edge,  this  line  is  broken  up  into  small  por- 
tions, so  as  to  appear  like  a  band  of  brilliant  points.    This  phenomenon 
is  called  Baily's  leads,  from  Mr.  Francis  Baily,  who  was  the  first  to 
describe  it  minutely,  in  1836.     This  is  supposed  to  be  caused  by  the 
irregularities  of  the  moon's  surface,  serrating  its  dark  edge,  and  pro- 
jected on  the  sun's  brilliant  disc. 

4.  Pink  or  rose-colored  protuberances  which  project  from  the  margin 
of  the  moon's  disc  when  the  obscuration  is  total.    One  measured  by 

QUESTIONS. — 193.  The  phenomena  connected  with  a  total  eclipse  ?  a.  Effect  on  igno- 
rant minds?  ft.  State  the  most  interesting  phenomena  presented  by  a  solar  eclipse? 
The  corona?  Baily's  beads?  Rose-colored  protuberances?  Explain  the  cause  cf  each. 


ECLIPSES.  141 

De  La  Rue,  in  1860,  was  found  to  be  at  least  44,000  miles  in  vertical 
height  above  the  sun's  surface.  They  have  been  seen  by  most  observ- 
ers. No  entirely  satisfactory  cause  has  been  assigned  for  these 
appearances,  although  it  seems  to  be  settled  that  their  origin  is  in 
the  sun  and  not  the  moon  ;  and  it  is  thought  by  some  that  they  are 
clouds  floating  in  the  atmosphere  of  the  sun,  their  peculiar  color  being 
caused  by  the  absorption  of  the  other  colors,  as  sometimes  occurs  in 
the  case  of  clouds  in  our  own  atmosphere. 

c.  Appearance  of  a  Lunar  Eclipse.— In  a  total  lunar  eclipse,  the 
moon  does  not  become  wholly  invisible,  but  assumes  a  dull,  reddish 
hue,  which  arises  from  the  refraction  of  the  sun's  rays  by  the  earth's 
atmosphere.     The  red  color  is  caused  by  the  absorption  of  the  blue 
rays  in  passing  through  the  atmosphere,  just  as  the  western  sky  as- 
sumes a  ruddy  hue  when  illuminated  in  the  evening  by  the  solar  light. 
Sometimes,  however,  it  happens  that  the  moon  is  rendered  very  nearly 
invisible,  as  was  the  case  in  1643  and  1816  ;  and  the  degree  of  distinct- 
ness of  the  moon's  appearance  varies  considerably  at  different  times, 
owing  to  the  different  conditions  of  the  atmosphere. 

d.  Earliest  Observations  of  Lunar  Eclipses. — These  were  made 
by  the  Chaldeans, — the  first  recorded  eclipse  having  taken  place  in  720 
B.C.    This  eclipse  was  total  at  Babylon,  and  occurred  about  9£  o'clock 
P.M.    The  record  of  the  occurrence  of  eclipses  is  often  very  useful  in 
fixing  the  dates  of  history. 

194.  An  OCCULTATION"  is  the  concealment  of  a  planet  or 
star  by  the  interposition  of  the  moon  or  some  other  body. 

The  occultation  of  a  planet  or  star  by  the  moon  is  a  very  interesting 
and  beautiful  phenomenon.  From  new  moon  to  fall  moon,  she 
advances  eastward  with  the  dark  edge  foremost,  so  that  the  occulted 
body  disappears  at  the  dark  edge  and  re-appears  at  the  enlightened 
edge.  In  the  other  part  of  her  orbit  this  is  reversed.  The  former 
phenomenon  is  of  course  the  more  striking,  the  star  or  planet  appear- 
ing to  be  extinguished  of  itself. 

QUESTIONS.— c.  Describe  the  appearance  of  a  lunar  eclipse,  d.  Earliest  observations 
—by  whom  made  ?  194.  What  is  an  occultation  ? 


CHAPTER   XI. 


THE  TIDES. 

195.  TIDES  are  the  alternate  rising  and  falling  of  the 
water  in  the  ocean,  bays,  rivers,  etc.,  occurring  twice  in  about 
twenty-five  hours. 

196.  FLOOD  TIDE  is  the  rising  of  the  water,  and  at  its 
highest  point  is  called  high  water.     EBB  TIDE  is  the  falling 
of  the  water,  and  at  its  lowest  point  is  called  loiv  water. 

197.  The  tides  are  caused  by  the  unequal  attraction  of  the 
sun  and  moon  upon  the  opposite  sides  of  the  earth. 

<l.  Since  the  attraction  of  gravitation  varies  inversely  as  the  square 
of  the  distance,  the  sun  and  moon  must  attract  the  water  on  the  side 
nearest  to  them  more  than  the  solid  mass  of  the  earth  ;  while  on  the 
side  farthest  from  them,  the  water  must  be  attracted  less  than  the 
solid  earth ;  hence,  there  must  be  a  tendency  in  the  water  to  rise  at 
each  of  these  points ;  it  being  drawn  away  from  the  earth  at  the  point 
toward  the  sun  or  moon,  and  the  earth  being  drawn  away  from  it  at 
the  other  point.  At  the  points  90°  from  these,  the  effect  of  the  attrac- 
tion is  just  the  reverse  ;  for  since  it  does  not  act  in  parallel  lines,  it 
tends  to  draw  together  the  two  sides  of  the  earth,  and  thus  compresses 
the  water  so  as  to  cause  it  to  recede,  and  hence  increases  its  tendency  to 
rise  at  the  other  points. 

Thus  at  A  (Fig.  91)  the  water  is  jittfaeted  by  the  sun  more  than  the 
earth,  and  at  B  less  ;  while  at  C  and  D  the  attraction  squeezes  in  the  water, 
as  it  were,  so  as  to  make  it  recede  still  more',  and  thus  to  augment  its  rising 
at  A  and  B.  It  will  be  obvious  that  the  attraction  of  the  moon  acts  so  as  to 
disturb  the  water  just  as  that  of  the  sun  does  ;  hence,  in  the  position  repre- 

QUESTIONS.— 195.  What  are  tides?  196.  What  is  flood  tide?  Ebbtide?  197.  How- 
are  the  tides  caused  ?  a.  How  many  points  of  the  earth's  surface  are  affected  simul- 
taneously ?  How  is  this  explained  ? 


THE    TIDES.  143 

sented  in  the  diagram,  when  the  moon  is  in  opposition,  the  action  of  both  the 
sun  and  moon  is  exerted  upon  the  same  points,  A,  B  and  C,  D ;  and  it  will 
also  be  obvious  that  if  the  moon  were  in  conjunction,  that  is,  on  the  same 
side  of  the  earth  as  the  sun,  the  effect  would  be  the  same,  because  the 
same  points  would  be  acted  upon. 

Fiff.  91. 


6.  From  the  above  explanation,  it  will  be  apparent  that  similar 
tides  must  occur  simultaneously  on  opposite  sides  of  the  earth  ;  namely, 
flood  tides  on  the  side  turned  toward  and  that  turned  from  the  sun  or 
moon,  and  ebb  tides  at  the  two  points  90°  distant. 

198.  Since  the  moon  is  so  much  nearer  to  the  earth  than 
the  sun  is,  its  attraction  on  the  opposite  sides  is  much  more 
unequal,  and  consequently  its  disturbing  action  is  greater. 
At  the  mean  distance  of  the  sun  and  moon  from  the  earth, 
the  disturbing  or  tidal  force  of  the  moon  is  about  2]  times 
that  of  the  sun. 

ft.  Considering  the  moon's  mean  distance  from  the  centre  of  the 
earth  238,000  miles,  and  the  earth's  diameter  8,000  miles,  the  moon 
must  attract  the  side  of  the  earth  nearest  to  her  more  than  the  oppo- 
site side  in  the  ratio  of  (234,000)*  to  (242,000)s ;  that  is,  as  1  to  1.07 
(nearly).  Hence,  the  moon's  disturbing  force  is  .07  of  her  own  attrac- 
tion. Taking  the  sun's  mean  distance  from  the  earth's  centre  at 
91,500,000  miles,  the  ratio  of  his  different  attractions  will  be  as 
(91,496,000)*  to  (91,504,000)*,  or  as  1  to  1.000175  (nearly) ;  that  is,  the 
sun's  disturbing  force  is  equal  to  .000175  of  his  own  attraction. 

QUESTIONS. —ft.  What  tides  occur  simultaneoiiRly  ?  198.  How  does  the  moon's  tidal 
force  compare  with  the  sun's  ?  a.  By  what  calculation  is  this  proved  ? 


144  THE    TIDES. 

Now,  the  mass  of  the  sun  is  about  25,200,000  times  that  of  the  moon 

25,200,000 
[315,000  X  80],  and  its  distance,  385  times  as  great  ;  hence,  ~-/6-  = 


170  (nearly)  will  be  the  force  of  the  sun  upon  the  earth,  the  moon's 
being  1  ;  in  other  words,  the  sun's  attraction  on  the  earth  is  to  the 
moon's  as  170  to  1.  Hence,  170  X  .000175,  which  is  equal  to  .02975,  is 
the  sun's  disturbing  force,  while  the  moon's,  as  above  shown,  is  .07  ; 
and  therefore  the  former  is  to  the  latter  as  .02975  to  .07,  or  as  1  to  2£. 
This  calculation  being  designed  merely  to  illustrate  the  principle,  is 
made  with  only  approximate  accuracy,  but  gives  the  true  result  as 
found  by  the  higher  mathematics.  Sir  Isaac  Newton  computed  this 
ratio  as  23  to  58,  or  1  to  2£,  by  calculations  based  upon  the  observed 
differences  of  the  height  of  spring  and  neap  tides. 

b.  In  the  above  calculation,  the  moon's  mass  is  supposed  to  be 
known,  and  is  made  use  of  to  determine  the  relative  forces  of  the  sun 
and  moon  ;  but,  practically,  the  problem  is  reversed,  the  comparative 
disturbance  of  the  two  bodies  being  deduced  by  observations  of  the 
tides  themselves,  and  then  employed  to  determine  the  moon's  mass. 

199.  When  the  sun  and  moon  are  on  the  same  or  oppo- 
site sides  of  the  earth,  they  unite  their  attractions,  and  thus 
raise  the  highest  flood  tides  at  the  points  under  or  opposite 
them  and  the  lowest  ebb  tides  at  the  points  90°  from  these. 
Such  tides  are  called  spring  tides  ;  and  they  occur  at  every 
new  and  full  moon,  or  a  short  time  afterward. 

200.  When  the  moon  is  in  quadrature,  its  tidal  force  is 
partly  counteracted   by   that  of    the   sun,   since  the  two 
forces    act  at  right    angles  with   each   other;    and  conse- 
quently the  water  neither  rises  so  high  at  flood,  nor  descends 
so  low  at  ebb  tide.     Such  tides  are  called  neap  tides  ;  they 
occur  when  the  moon  is  in  either  of  the  quarters. 

Fig.  92  represents  neap  tide.  The  effect  of  the  sun  at  A  and  B,  and  of 
the  moon  at  C  and  D,  is  to  equalize  the  height  of  the  water  all  over  the 
earth.  The  pupil  must  understand  in  inspecting  these  diagrams,  that  the 
actual  effect  of  the  sun  or  moon  is  not,  by  any  means,  so  great  as  is  repre- 

QUESTIONS.  —  ft.  Practically,  is  this  computed  from  the  moon's  mass?  199.  What  are 
spring  tides?  How  caused?  200.  What  are  neap  tides?  How  caused?  When  do 
spring  and  neap  tides  occur  ? 


THE    TIDES.  145 

sented.    It  is,  in  fact,  but  a  few  feet,  while  the  earth's  diameter  is  nearly 
8,000  miles.  * 

Fig.  92. 


«.  Since  the  tidal  force  of  the  moon  is  so  much  greater  than  that  of 
the  sun,  it  is  the  passage  of  the  former  across  the  meridian  that  deter- 
mines the  rising  of  the  tide  at  any  place,  this  lunar  tide  being  either 
augmented  or  diminished  by  the  inferior  tidal  force  of  the  sun. 

b.  The  tides  not  only  vary  according  to  the  position  of  the  moon 
with  regard  to  the  sun,  but  are  sensibly  affected  by  the  variations  in 
the  distance  of  the  moon  from  the  earth,  increasing  and  diminishing 
inversely  with  it,  but  in  a  more  rapid  ratio. 

c.  The  height  of  the  spring  tides  is  to  that  of  the  neap  tides,  gen- 
erally, as  2^  to  1.     For  spring  tide  is  the  result  of  the  sum  of  the 
moon  and  sun's  forces,  or  2^  -f-  1  =  3£  ;  and  neap  tide,  the  result  of 
the  difference,  or  2i  —  1  =  1£  ;  and  3f,  :  H  : :  2^  :  1.      This  varies  at 
different  places ;  at  Brest,  in  France,  the  spring  tides  rise  to  the  height 
of  over  19  feet,  and  the  neap  tides  about  9  feet.    On  the  Atlantic  coast 
of  the  United  States,  the  height  of  the  former  is  to  that  of  the  latter 
as  3  to  2. 

d.  In  the  northern  hemisphere,  the  highest  tides  occur  during  the 
day  in  summer,  and  during  the  night  in  winter  ;  but  in  the  southern 
hemisphere  this  is  reversed. 

This  will  be  apparent  from  an  inspection  of  Fig.  91.    The  greatest  tidal 

QUESTIONS. — a.  What  determines  the  rising  of  the  tide  at  any  place  ?  b.  What 
additional  cause  of  variation  in  the  tides?  c.  How  does  the  height  of  spring  tides 
compare  with  that  of  neap  tides  ?  d.  What  difference  between  the  diurnal  and  noctur- 
nal tides?  Why? 


146  THE    TIDES. 

elevation  of  the  water  is  of  course  at  A  and  B,  and  diminishes  north  and 
south  of  these  points.  At  a  the  elevation  of  the  water  is  obviously  greater 
than  at  6;  but  a  is  the  position  of  a  place  in  the  northern  hemisphere,  at 
noon,  and  in  summer,  since  the  axis  is  turned  toward  the  sun,  and  &,  its 
position  at  midnight ;  so  that  the  tide  is  higher  during  the  day  than  during 
the  night,  in  this  season.  Conceive  the  axis  turned  the  other  way,  and  it 
will  be  at  once  seen  that  the  reverse  is  true  in  winter. 

e.  The  height  of  the  tide,  therefore,  varies  with  the  declinations  of 
the  sun  and  moon,  being  greater  in  proportion  as  the  two  bodies  are 
near  the  equator.  If  at  the  time  of  the  equinoxes  the  moon  happens  to 
be  near  the  equator,  the  tides  are  the  highest  of  all,  and  are  called  the 
Equinoctial  Spring  Tides. 

201.  The  tides  do  not  rise  at  the  same  hour  every  day,  but 
generally  about  50  minutes  later;   because,  as  the  moon 
advances  in  her  orbit,  the  same  place  on  the  earth's  surface 
does  not  come  again  under  the  moon  until  about  50  min- 
utes later  than  on  the  previous  day. 

a.  The  interval  which  elapses  from  the  moon's  passing  the  merid- 
ian of  a  place  until  it  returns  to  the  same  again  is  24h  50m  28* ;  the 
interval,  therefore,  between  two  successive  tides  is  12b  25m  14§.  This 
is  not,  however,  always  the  true  interval,  from  circumstances  which 
will  be  explained  hereafter. 

202.  The  tide  does  not  generally  rise  until  two  or  three 
hours  after  the  moon  has  passed  the  meridian  ;  because,  on 
account  of  its  inertia,  the  water  does  not  immediately  yield 
to  the  action  of  the  sun  or  moon. 

a.  By  inertia  is  meant  the  resistance  which  matter  of  every  kind 
makes  to  a  change  of  state,  whether  of  rest  or  motion ;  that  is,  it  can  not 
put  itself  in  motion,  neither  can  it  stop  itself.    The  tides  are  not  only 
retarded  by  inertia,  but,  to  some  extent,  by  the  friction  on  the  bed  of 
the  ocean  or  the  sea,  or  the  sides  of  rivers  and  confined  channels* 

b.  Solar  and  Lunar  Tide  Waves. — The  solar  tide  wave  is  more 
retarded  than  the  lunar,  since  the  tidal  force  of  the  sun  is  so  much 

QTTEBTIONS.— e.  Equinoctial  spring  tides?  201.  Why  do  the  tides  rise  later  from  day 
to  day?  202.  Why  are  the  tides  behind  the  moon  ?  a.  Inertia  ?  b.  Which  tide  waves 
are  more  retarded,  the  solar  or  lunar?  What  is  meant  by  the  priming  and  lagging  of 
the  tides? 


THE    TIDES.  147 

feebler  than  that  of  the  moon.  The  general  retardation  of  the  tides 
depends  on  the  relative  position  of  the  solar  and  lunar  tide  waves.  At 
new  and  full  moon  the  solar  tide  wave,  being  more  retarded,  is  east  of 
the  lunar  ;  and,  therefore,  high  water,  which  results  from  the  union  of 
the  two  waves,  must  be  east  of  the  place  it  would  have  been  if  the 
moon  had  acted  alone ;  and  hence,  on  this  account,  the  tide  will  rise 
later.  When,  however,  the  moon  is  in  either  of  the  quarters,  the 
solar  tide  wave  is  west  of  the  lunar,  and  the  tide  rises  earlier.  This  is 
called  the  priming  and  lagging  of  the  tides  ;  since  it  either  shortens  or 
lengthens  the  tidal  day  of  24h  5001  28' .  The  highest  spring  tide  rises 
when  the  moon  passes  the  meridian  about  lih  after  the  sun ;  for  then 
the  two  tide  waves  immediately  coincide, 

c.  These  tide  waves  are  not  to  be  conceived  as  currents  moving  pro- 
gressively through  the  ocean,  but  as  undulations  rising  nearly  under 
the  sun  and  moon,  and,  as  the  earth  turns  on  its  axis,  moving  westward 
over  its  surface,  at  the  same  rate.    This  would  be  the  case  exactly,  and 
at  all  parts  of  the  earth,  if  it  were  uniformly  covered  with  water,  so 
that  the  great  tide  wave  could  move  without  any  obstruction  from  oppos- 
ing shores.     In  the  open  ocean  it  constantly  follows  the  moon  at  the 
distance  of  about  30°  from  her  ;  but  the  tide  rises  at  every  place  at  a 
different  time  owing  to  the  peculiarities  of  its  situation.    Lines  drawn 
on  the  map  or  globe  through  all  the  adjacent  places  which  have  high 
water  at  the  same  time,  are  called  cotidal  lines. 

d.  The  average  interval  of  time  between  noon  and  the  time  of  high 
water  at  any  port  on   the  days  of  new  and  full  moon,  is  called  the 
establishment  of  the  port.    The  mean  establishment  of  New  York  is 
about  8i  hours    of  Boston,  Hi  hours ,  of  San  Francisco,  12|  hours. 

203.  The  tides  that  occur  in  rivers,  narrow  bays,  or  other 
bodies  of  water  at  a  distance  from  the  ocean,  are  not  caused 
by  the  immediate  action  of  the  sun  and  moon,  but  arise  from 
the  undulations  of  the  great  ocean  tide  wave,  urging  the 
water  into  these  contracted  inlets.  The  tides  of  the  ocean 
are  called  primitive  tides  ;  those  of  rivers,  inlets,  etc.,  are 
called  derivative  tides. 

QUESTIONS.— c.  Do  the  tides  rise  at  the  same  time  at  all  places?    Why  not?    203 
What  are  primitive  tides  ?    Derivative  tides  ? 


148  THE    TIDES. 

204.  The  average  height  of  the  tide  for  the  whole  globe  is 
about  2:J  feet ;  and  this  is  the  height  to  which  it  rises  in  the 
ocean.  The  height,  however,  at  any  particular  place  de- 
pends upon  its  situation;  the  highest  tides  occurring  in 
narrow  bays,  and  arms  of  the  sea  running  up  into  the  land. 
Lakes  have  no  perceptible  tides. 

a.  The  highest  tides  in  the  world  take  place  in  the  Bay  of  Fundy, 
the  mouth  of  which  is  exposed  to  the  great  Atlantic  tide  wave.  At 
the  head  of  the  bay  the  ordinary  spring  tides  rise  to  the  height  of  50 
feet,  while  special  tides  have  been  known  to  rise  as  high  as  70  feet. 
In  New  York,  the  height  of  the  tide  is,  at  its  maximum,  about  8  feet ; 
in  Boston,  11  feet.  On  the  other  hand,  at  some  places  there  is  scarcely 
any  tide  at  all.  An  instance  of  this  is  found  at  a  point  on  the  south- 
eastern coast  of  Ireland,  the  tide  stream  being  diverted  to  the  opposite 
shore  by  a  promontory  at  the  entrance  of  St.  George's  Channel. 

ft.  Velocity  of  the  Tide- Wave. — This  is  affected  by  various  cir 
cumstances ;  such  as  the  depth  of  the  water,  the  obstructions  from 
opposing  shores,  etc.  The  moon  tends  to  draw  the  water  along  with 
it  at  the  rate  of  1,000  miles  an  hour  at  the  equator  ;  but  the  actual 
rate  of  movement  is  much  less  rapid.  The  tide  wave  requires  about 
40  hours  to  reach  the  Atlantic  coast  from  the  south-eastern  Pacific, 
where  it  originates,  traversing  the  Pacific,  Indian,  and  South  Atlantic 
oceans.  When  it  strikes  the  shallow  waters  of  the  coast  its  velocity  is 
greatly  diminished,  not  exceeding,  sometimes,  50  miles  an  hour.  Its 
breadth  is,  of  course,  diminished  with  its  velocity.  At  a  velocity  of 
600  miles  an  hour,  its  breadth  would  be  over  7,000  miles  ;  but  when 
the  velocity  is  reduced  to  100  miles  an  hour,  its  breadth  is  only  about 
1200  miles. 

€.  Atmospheric  Tides.— The  same  causes  that  act  to  disturb  the 
ocean  must  also  produce  similar  disturbances  in  the  atmosphere.  The 
atmospheric  tides,  however,  have  been  demonstrated  by  Laplace  to 
be  very  inconsiderable  in  height,  not  exceeding,  at  Paris,  one-thou- 
sandth of  an  inch, — an  amount  far  too  small  to  be  indicated  by 
ordinary  observations  with  the  barometer. 

QUESTIONS.— 204.  What  is  the  average  height  of  the  water  for  the  whole  globe  ?  On 
what  does  the  height  at  particular  places  depend?  «.  Where  are  the  highest  tides? 
Why  '!  b.  Velocity  of  the  tide  wave  ?  e.  Atmospheric  tides  ? 


CHAPTER  XII. 

THE    INFERIOR    PLANETS. 
I.  MERCURY.      $ 

205.  MERCURY  is  remarkable  for  its  small  size,  its  swift 
motion,  and  the  great  inclination  and  eccentricity  of  its 
orbit.  It  is,  as  far  as  is  positively  known,  the  nearest  planet 
to  the  sun. 

(l.  Name  and  Sign. — This  planet  probably  derived  its  name  from 
the  swiftness  of  its  motion,  Mercury  being,  in  the  heathen  mythology, 
the  "  messenger  of  the  gods."  The  sign  <?  is  supposed  to  represent 
the  caduceus,  or  wand,  which  the  god  is  always  seen,  in  the  pictures 
of  him,  to  carry  in  his  hand. 

b.  Vulcan. — Reference  is  made  in  Art.  16  to  a  planet  supposed  by 
some  to  exist  between  Mercury  and  the  sun  ;  the  following  are  the  cir- 
cumstances connected  with  its  supposed  discovery  . — On  the  26th  of 
March,  1859,  a  small  dark  body  was  seen  to  pass  over  a  portion  of  the 
sun's  disc,  by  M.  Lescarbault,  a  French  physician,  but  an  amateur  of  as- 
tronomy ;  and  this  appeared  to  him  to  indicate  the  existence  of  a  planet 
whose  orbit  must  be  included  within  that  of  Mercury.  From  the 
observations  which  he  made  with  his  rude  instruments,  he  calculated 
its  period  at  about  20  days ,  its,  distanpe,  14,000,000  miles ;  and  the 
inclination  of  its  orbit,  about  12°.  0?i  publishing  this  fact,  the  cele- 
brated French  astronomer  and  mathematician,  Leverrier,  visited  him, 
and  after  closely  questioning  him  as  to  his  means  and  method  of 
observation,  was  completely  satisfied  of  the  truth  of  his  statements 
Singular  to  say,  however,  no  other  observer  has  been  able  to  detect 
any  indications,  of  such  a  planet ;  but,  on  the  contrary,  M.  Liais,  an 

QUESTION g.— 205.  For  what  is  Mercury  remarkable  ?  a.  Its  name  and  sign  ?  6. 
Supposed  discovery  of  Vulcan? 


150  MEKCUKY. 

astronomer  of  skill  and  experience,  who  happened  to  be  engaged  in 
observations  of  the  sun,  at  Rio  Janeiro,  at  the  identical  moment  of  M. 
Lescarbault's  alleged  discovery,  asserted  positively  that  no  planetary 
object  was  visible  at  that  time.  The  existence  of  any  planet  inferior 
to  Mercury  is  therefore  considered  very  doubtful. 

206.  Mercury  and  Venus  are  known  to  be  inferior  planets, 

1.  Because  their  greatest  elongation  is  always  less  than  90°  ; 

2.  Because  they  exhibit  all  the  different  phases  which  are 
presented  by  the  moon ;  and,  3.  Because  they  are  seen,  at 
the  time  of  a  transit,  to  pass  across  the  sun's  disc. 

(i.  A  superior  planet  also  exhibits  phases,  but  it  must  always  show 
more  than  half  the  disc  ,  that  is,  it  must  present  the  full  or  gibbous  form. 
An  inferior  planet,  however,  in  passing  between  the  points  of  extreme 
elongation,  presents  the  crescent  form,  and,  in  inferior  conjunction, 
either  totally  disappears  or  is  projected,  in  the  form  of  a  small  round 
black  spot,  upon  the  disc  of  the  sun. 

207.  The  greatest  angular  distance  of  an  inferior  planet 
from  the  sun,  during  any  single  revolution,  is  called  its 
extreme  elongation.      The  greatest   extreme   elongation   of 
Mercury  is  28|°  ;  the  least,  18°. 

a.  This  large  variation  in  the  extreme  elongation  is  an  indication 
that  Mercury  revolves  in  an  orbit  of  considerable  ellipticity,  since 
this  angle  depends  upon  the  relative .  distances  of  Mercury  and  the 
earth  from  the  sun.  It  must  be  greatest  when  the  earth  is  in  perihe- 
lion and  Mercury  in  aphelion,  and  least  when  the  earth  is  in  aphelion 
and  Mercury  in  perihelion ;  while  the  mean  distance  of  each  would 
give  the  mean  value  of  this  elemerjt. 

In  Fig  93  let  S  be  the  sun,  E,  the  earth,  and  M,  Mercury  at  the  point  of 
extreme  elongation,  M  E  being  tangent  to  the  orbit,  and  S  M  E  a  right 
angle.  It  will  be  obvious  that  M  E  S,  the  angle  of  extreme  elongation, 
will  be  at  its  maximum  when  S  E  is  the  shortest  and  S  M  the  longest ;  and 
at  its  minimum  when  these  are  reversed  ;  because  its  size  depends  upon 


QUESTIONS. — 206.  How  are  Mercury  and  Venus  known  to  be  inferior  planets?  a. 
What  phases  do  the  inferior  and  superior  planets  present  ?  207.  Extreme  elongation  * 
What  is  it  in  the  case  of  Mercury?  a.  Why  so  variable?  Give  the  calculation  from 
the  diagram. 


MERCURY. 


151 


the  ratio  of  S  M  to  S  E,  being  greatest  when  Fig'  9a 

the  ratio  is  greatest.  The  perihelion  dis- 
tance of  the  earth  is  about  90,000,000  miles, 
the  aphelion  distance  of  Mercury  is  about 
42,600,000  miles.  For  these  values  the  ratio 
of  S  M  to  S  E  would  be  about  .473 ;  and  the 
angle  corresponding  to  this  is  28°  IS7.  The 
least  ratio  of  these  lines  is  .3,  and  hence,  the 
least  angle,  18° ;  while  the  mean  ratio  is  .387 
(nearly),  indicating  an  angle  of  22°  47', 
which  is  therefore  the  mean  value  of  this 
element. 

208.  The  aphelion  distance  of  Mercury  from  the  sun  is 
about  42,600,000  miles ;  its  perihelion  distance,  28,100,000 
miles ;  and  its  mean  distance,  therefore,  nearly  35,400,000 
miles. 

a.  The  Distance  Calculated — The  distance  of  an  inferior  planet 
can  be  determined  by  its  extreme  elongation  ;    for  (Fig.  93)  S  M  is 
equal  to  S  E  multiplied  by  the  sine  of  the  angle  S  E  M.      Now,  if  the 
angle  is  28°  15',  its  sine  (or  ratio  of  S  M  to  S  E)  will  be  .473,  and  hence, 
taking    the    perihelion    distance  of   the    earth,  90,000,000  X  .473  = 
42,600,000,  which  is  the  aphelion  distance  of  Mercury. 

b.  The  mean  distance  of  any  planet  from,  the  sun  can  be  calculated 
by  Kepler's  third  law,  when  we  know  the  sidereal  period.     In  the  case 
of  Mercury,  this  is  very  nearly  88  days  ;  and  hence,  as  the  squares  of 
tlie  periodic  times  are  in  proportion  to  the  cubes  of  the  mean  distances, 
(365|)»  :(88)2 :  :(91,500,000)3 :  the  cube  of  the  mean  distance  of  Mercury, 
which,  if  the  proportion  be  worked  out  and  the  cube  root  extracted, 
will  give  35,400,000  (nearly) ;  and  this  is  the  true  value  of  this  ele- 
ment.     [If  the  pupil  is  sufficiently  advanced,  it  will  be  well  for  the 
teacher  to  show  how  this  calculation  may  be  facilitated  by  employing 
a  table  of  common  logarithms.] 

c.  The  difference  between  the  aphelion  and  perihelion  distances  of 
Mercury,  it  will  be  seen,  is  14,500,000  ;  hence  its  eccentricity  is  7,250,- 
000  miles,  which  is  nearly  .205  of  its  mean  distance,  or  about  12  times 
as  great  as  that  of  the  earth. 


QursTioNS.— 20S.  What  are  the  aphelion,  perihelion,  and  mean  distances  of  Mercury  ? 
a.  How  calculated  ?  b.  How  determined  by  Kepler's  third  law  ?  c.  Eccentricity — ho^r 
found  ? 


152  MERCURY. 

209.  The  apparent  diameter  of  Mercury,  when  greatest, 
is  about  13  seconds,  and  when  least,  about  4^  seconds  ;  this 
difference  being  caused  by  the  variations  in  its  distance 
from  the  earth. 

a.  When  in  inferior  conjunction  it  is,  of  course,  at  the  point  nearest 
to  the  earth,  and  when  in  superior  conjunction,  at  its  farthest  point 
from  the  earth.  When  Mercury  is  in  superior  conjunction  and  each 
planet  is  at  its  aphelion,  they  are  the  farthest  possible  from  each  other  ; 
that  is,  42,600,000  +  93,000,000  =  135,600,000  miles.  When  Mercury 
is  in  inferior  conjunction  and  at  its  aphelion,  while  the  earth  is  in 
its  perihelion,  they  are  nearest  to  each  other  ;  that  is,  90,000,000  — 
42,600,000  =  47,400,000  miles. 

210.  The  real  diameter  of  Mercury  is  about  3,000  miles 
(more  exactly,  2,962  miles). 

a.  This  is  deduced  from  its  distance  and  apparent  diameter  by  the 
method  explained  in  Art.  147,  a.     Suppose  the  apparent  diameter  is 
ascertained  to  be  1|^',  while  its  distance  from  the  earth  is  50,000,000 
miles.     Then,  the  sine  of"6i",  which  is  .00002962,  being  multiplied  by 
50,000,000  gives  14pl^  the  Semi-diameter.  * 

b.  A  clearer  idea,  may  be  formed  of  the  apparent  diameter  of  a 
planet  by  comparing  it  with  that  of  the  moon,  which  subtends  an 
angle  of  more  than  1,800"  ;  consequently,  Mercury,  when  it  appears 
as  a  thin  crescent  near  inferior  conjunction,  subtends  an  angle  equal  to 
only  about  ,-^ff  or  -,-£0-  part  of  the  moon's  disc  ;  while  when  it  recedes 
to  its  greatest  distance,  it  is  about  -^  part. 

c.  The  oblateness  of  the  planet  has  been  generally  considered  very 
email  ;  but  one  astronomer  (Dawes),  in  1848,  gave  it  at  ^,  which  would 

Tig.  94.  be  nearly  ten  times  as  great  as  that  of  the 

earth. 

d.  Volume,  Mass,  and  Density  —  The 
volume  of  Mercury  is  about  ,052  of  the 
earth's  ;  and  the  mass  has  been  estimated 

COMPABATIVE  VOICES  OF  HEB-    *t  about  -083  ;  hence,  its  density  must  be 
CUBY  AND  THE  BABTH.  .063  -*-  .052  =  1.12,    the   earth's  being  1  ; 


QUESTIONS.—  209.  What  is  the  apparent  diameter  when  greatest?  When  least?  a. 
Why  so  variable  ?  210.  What  is  the  real  diameter?  a.  How  found  ?  b.  How  does  it 
compare  with  that  of  the  moon?  e.  Is  Mercury  oblate  ?  rf.  What  is  its  volume? 
Mass?  Density? 


MERCURY.  153 

and  since  this  is  5.67  of  water,  5.67  X  1.12  =  6.35,  must  be  the  density 
as  compared  with  water.  To  find  the  mass  of  Mercury  is  so  difficult 
a  problem,  that  these  figures  can  not  altogether  be  relied  on.  There 
is  but  little  doubt,  however,  that  its  density  exceeds  that  of  the 
earth  by  an  eighth  to  a  fifth.  The  famous  French  mathematician  Le 
Verrier  estimates  it  at  more  than  twice  that  of  the  earth. 

e.  Superficial  Gravity  at  Mercury. — Since  gravity  varies  directly 
as  the  quantity  of  matter,  and  inversely  as  the  square  of  the  distance 
from  the  centre,  at  the  surface  of  Mercury  it  must  be  nearly  (j£S$)2  X 
.063,  or  V  X  .063  =  .448  (nearly).  Hence,  a  body  that  weighs  a  pound 
at  the  surface  of  the  earth  would  weigh  less  than  half  a  pound  at 
Mercury.  If  we  should  be  transported  to  this  planet,  we  should  ap- 
pear to  have  more  than  twice  as  much  muscular  power,  since  the 
resistance  to  our  efforts  would  be  diminished  more  than  one-half. 

211.  Mercury  is  supposed  to  perform  a  diurnal  rotation 
in  about  24  hours  (24h  5m  28* ). 

a.  This  was    discovered   by  the  celebrated  German  astronomer, 
Schroeter,  at  the  end  of  the  last  century,  by  examining  daily  the  ap- 
pearance of  the  cusps,  or  extremities  of  the  crescent   form  of  the 
planet,  which  instead  of  being  pointed  are  sometimes  obtuse,  owing  to 
irregularities  on  the  surface  of  the  planet,  and  during  one  rotation 
undergo  certain  changes  in  form,  which  enabled  the  astronomer  to  dis- 
cover the  period.     He  also  thought  that  he  had  discovered  certain  dark 
bands  across  the  disc,  and  was  enabled  to  measure  the  height  of  some 
of  the  mountains,  which,  according  to  his  computations,  are  very  high, 
some  of  them  more  than  ten  miles, — an  enormous  altitude  for  so  small  a 
body.     These  discoveries  have  not,  however,  been  confirmed  by  the 
observations  of  other  astronomers.      Sir  John  Herochel,  with  all  his 
advantages  for  telescopic  observation,  and  his  great  experience  and  skill 
as  an  observer,  states  that  "  all  that  can  be  certainly  affirmed  of  Mer- 
cury is,  that  it  is  globular  in  form  and  exhibits  phases  ;  and  that  it  is 
tco  small  and  too  much  lost  in  the  constant  and  close  effulgence  of  the 
sun  to  alljw  the  further  discovery  of  its  physical  condition." 

b.  Mercury  is  a  very  difficult  object  to  see  in  consequence  of  its 
nearness  to  the  sun ;  for  it  is  generally  entirely  involved  in  the  twi- 
light or  obscured  by  the  mists  that  float  near  the  horizon.     Copernicus, 

QUESTIONS.— e.  How  does  gravity,  or  weight,  at  Mercury  compare  with  that  at  the 
e.-irth?  211.  In  what  time  does  Mercury  rotate  ?  a.  How  and  by  whom  was  this  dis- 
covered ?  &.  Why  is  Mercury  a  difficult  object  to  see  ? 


154  MERCURY. 

it  is  said,  regretted  at  his  death  that  he  had  never  been  able  to  obtain 
a  view  of  it.  In  lower  latitudes,  where  the  diurnal  circles  are  more 
nearly  vertical,  the  twilight  shorter,  and  the  atmosphere  less  clouded, 
it  is  more  easily  seen.  The  fact  that  it  was  so  well  known  to  the 
ancients  as  a  planetary  body  proves  to  us  that  they  were  very  careful 
and  diligent  observers.  When  viewed  through  a  telescope,  it  looks 
intensely  brilliant,  on  account  of  its  proximity  to  the  sun  ;  and  this 
excessive  brilliancy  serves  to  prevent  the  clear  observation  of  any  spots 
on  the  disc  which  would  afford  positive  indications  of  its  axial  rotation. 
It  has,  nevertheless,  been  very  diligently  observed  by  astronomers. 
Arago  states  that  at  the  observatory  of  Paris  alone,  more  than  two  hun- 
dred complete  observations  of  it  were  made  from  1836  to  1842. 

212.  Mercury  performs  its  sidereal  revolution  in  about  88 
days  (87d  23h  16m) ;  its  synodic  period  is  about  116  days. 

a.  The  sidereal  period  may  be  ascertained  by  observing  when  the 
planet  is  at  either  node,  and  noticing  the  interval  of  time  that  elapses 
before  it  returns  to  the  same  node.  The  synodic  period  can  be  cal- 
culated on  the  principle  already  explained.  Thus,  365^  days-r- 
87.968  days  =  4.152,  which  is  the  number  of  sidereal  revolutions  in  a 
year  ;  hence  there  must  be  3.152  synodic  revolutions,  or  one  less  than 
the  sidereal ;  and  365^  days  -f-  3.152  =  116  days  (nearly). 

Or  the  synodic  period  may  be  found  by  observation,  and  the  sidereal 
period  deduced  from  it  on  the  same  principle.  (365  ^  -r- 116  =  3.152  /. 
365i-f-  4.152  =  87.968.) 

213.  The  apparent  diameter  of  the  sun  as  seen  at  Mer- 
cury varies  considerably,  owing  to  the  great  difference  in  its 
distance  at  aphelion  and  perihelion.     When  in  the  former 
position  it  is  nearly  69' ;  in  the  latter,  104' ;  being  when 
least  more  than  twice,  and  when  greatest  more  than  3| 
times  that  of  the  sun  as  seen  from  the  earth. 

a.  Light  and  Heat  at  Mercury. — The  light  and  heat  received 
from  the  sun  when  Mercury  is  in  perihelion  must  be  greater  than  in 
aphelion,  in  the  proportion  of  2.27  to  1  ;  that  is,  in  the  former,  about 
2|  times  as  great  as  in  the  latter ;  for  the  light  and  heat  vary  in 

QUESTIONS.— 212.  What  is  the  sidereal  period  of  Mercury?  Its  synodic  period  ?  a. 
How  may  one  be  deduced  from  the  other  ?  213.  Apparent  diameter  of  the  sun  at  Mer- 
cury ?  a.  Its  light  aud  heat  ? 


MEECUEY.  155 

proportion  to  the  area  of  the  sun's  disc,  and  this  is  as  the  square  of 
the  apparent  diameters ;  or  as  (104)2  to  (69)2,  or  as  2.27  to  1.  On  the 
same  principle,  the  average  amount  of  light  and  heat  received  by 
Mercury,  is  to  that  received  by  the  earth  as  the  square  of  the  mean 
apparent  diameter  of  the  sun  at  that  planet  (83')2  is  to  that  at  the  earth 
(32')2 ;  that  is,  as  6889  is  to  1024  or  as  6f  (nearly)  to  1.  In  other  words, 
the  light  and  heat  at  Mercury  are  nearly  6|  times  as  great  as  at  the 
earth.  This,  of  course,  may  be  very  much  modified  by  other  circum- 
stances. 

b.  Seasons  at  Mercury. — Since  the  light  and  heat  are  more  than  2 \ 
times  as  great  in  perihelion  as  in  aphelion,  there  must  be  a  succession 
of  seasons  on  the  planet  depending  entirely  on  the  eccentricity  of  its 
orbit,  summer  occurring  when  the  planet  is  in  perihelion,  and  winter 
when  it  is  in  aphelion.  If  the  axis  of  the  planet  is  inclined  to  its 
orbit,  another  succession  of  seasons  must  occur,  which,  if  they  coincide 
with  the  former,  must,  in  one  hemisphere,  augment  the  intensity  of  the 
heat,  and  in  the  other,  increase  that  of  the  cold  ;  while,  if  they  do  not 
coincide,  the  one  cause  must  tend  to  counteract  the  effects  of  the  other, 
and  thus  diminish  the  great  extremes  of  heat  and  cold. 

214.  TEANSITS  OF  MEECUET. — When  the  latitude  of  Mer- 
cury or  Venus,  at  the  time  of  inferior  conjunction,  is  less 
than  the  semi-diameter  of  the  sun,  a  transit  must  occur, 
the  planet  appearing  on  the  sun's  disc  like  a  small,  round, 
and  intensely  black  spot,  and  moving  across  it  from  east  to 
west. 

a.  It  appears  to  move  across  the  disc  from  east  to  west  for  the  same 
reason  that  the  solar  spots  appear  to  move  in  that  direction  (Art.  152,  6). 
The  planet's  velocity  being  faster  than  the  earth's,  the  planet  passes 
the  earth  actually  from  west  to  east,  but  in  a  direction  opposite  to  the 
diurnal  motion  of  that  part  of  the  earth  on  which  the  observer  stands ; 
hence  the  apparent  motion  is  westward,  since  east  is  in  the  direction 
of  the  rising  sun,  and  this  must  be  the  point  toward  which  any  place 
on  the  earth  turns. 

ft.  Transit  Limits.— The  limits  in  latitude  within  which  a  transit 
can  occur  correspond  to  the  semi-diameter  of  the  sun ;  and  as  Mer- 

QUESTIONS.— b.  Seasons  at  Mercury  ?  214  When  do  transits  occur  ?  a.  Appearance 
of  the  transit?  Why  does  the  planet  appear  to  move  from  east  to  west?  b.  What 
are  the  transit  limits? 


156  VENUS. 

cury's  orbit  is  inclined  to  the  ecliptic  at  an  angle  of  7°,  it  can  easily  be 
computed  that  the  planet,  at  inferior  conjunction,  must  be  within 
about  2°  of  longitude  from  the  node  for  a  transit  to  occur. 

c.  Times  of  the  Occurrence  of  Transits. — The  longitudes  of 
Mercury's  nodes  are  46°  ( ft )  and  226°  ( tf ) ;  hence  they  are  in  Taurus 
and  Scorpio,  and  the  earth  arrives  at  the  Jine  of  nodes  in  May  and 
November  of  each  year.  Transits  must,  consequently,  occur  in  these 
months ;  and  this  will  continue  to  be  the  case  for  a  long  time, 
because  the  nodes  change  their  position  on  the  ecliptic  only  about  13' 
in  a  century.  Because  7  sidereal  periods  of  the  earth  are  very  nearly 
equal  to  29  (29.064)  of  those  of  Mercury ;  and  13  of  the  former  are 
nearly  equal  to  54  (53.98)  of  the  latter,  transits  must,  as  a  general 
thing,  occur  at  intervals  of  7  or  13  years,  at  the  same  node.  Owing, 
however,  to  the  great  inclination  of  the  orbit,  and  the  consequent 
small  transit  limit,  these  periods  can  not  be  relied  on ;  and  it  requires  a 
period  of  217  years  to  bring  round  the  transits  exactly  in  the  same 
order.  The  last  transit  occurred  on  the  12th  of  November,  1861 ;  the 
next  will  occur  on  the  5th  of  November,  1868. 

II.   VENUS.      ? 

215.  VENUS  is  in  appearance  the  most  brilliant  and  beau- 
tiful of  all  the  planets,  and  is  remarkable    for  its  close 
resemblance  to  the  earth,  both  in  size  and  mass. 

a.  Name  and  Sign. — Venus,  in  the  pagan  mythology  and  religion, 
was  the  goddess  of  beauty,  and  hence  the  name  was  appropriately 
applied  to  the  most  beautiful  of  the  planets.  The  sign  is  sup- 
posed to  represent  a  mirror  having  a  handle  at  the  bottom.  By  the 
ancients,  this  planet,  when  an  evening  star,  was  called  Hesperus  or 
Vesper,  the  former  being  a  Greek  word,  and  the  latter  a  Latin  word, 
each  meaning  the  evening.  When  a  morning  star,  it  was  called 
Phosphorus  or  Lucifer,  the  former,  in  Greek,  signifying  that  which 
brings  the  light ;  and  the  latter  meaning  the  same  thing  in  Latin. 
These  were  at  first  supposed  to  be  different  bodies. 

216.  The  PHASES  of  Venus  exactly  resemble  those  of  the 


QUESTIONS.— c.  In  what  months  do  transits  occur  ?  Why  ?  At  what  intervals  do  they 
occur?  Why?  215.  For  what  is  Venus  remarkable?  a.  Its  name  and  sign?  216. 
Wfcat  phases  does  it  exhibit? 


VENUS. 


157 


moon,  and  when  viewed  with  a  telescope  are  very  interest- 
ing and  beautiful,  clearly  proving  that  this  planet  revolves 
within  the  earth's  orbit. 

217.  When  the  planet  is  in  superior  conjunction  its  full 
disc  is  visible,  which    gradually  diminishes  until,  at  the 
time  of  greatest  elongation,  only  half  of  the  disc  is  seen ; 
after  which  the  planet  still  continues  to  wane  until,  when 
near  inferior  conjunction,  it  assumes  the  form  of  a  slender 
crescent. 

218.  When  the  planet  is  full,  its  apparent  diameter  is  least, 
since  it  is  then  farthest  from  the  earth ;  but  near  inferior 
conjunction,  its  apparent  diameter  is  greater  than  at  any 
other  time,  except  when  it  is  seen  during  a  transit. 

The  accompanying  diagram  (Fig.  95)  shows  the  phases  of  Venus  during 
one  synodic  period.  The  difference  in  size  when  the  planet  is  full  and 
when  it  has  the  crescent  form,  will  be  obvious.  This  difference,  however, 

Fig.  95. 


PHASES  OF  VENUS. 

is  greater  than  here  presented ;  the  apparent  diameter  in  inferior  conjuction 
being  more  than  six  times  as  great  as  it  is  when  in  superior  conjunction. 

QTTESTIONS.— 21T.  When  is  it  full,  half,  and  crescent  ?    218.  When  is  its  apparent 
diameter  greatest  ?    When  least  ? 


158  VENUS. 

219.  The   extreme  elongation  of  Venus  never  exceeds 
47|°,  its  average  being  about  46°. 

a.  This  small  amount  of  variation  indicates  that  the  orbit  has  very 
little  eccentricity. 

b.  Venus  is  most  brilliant  when  the  elongation  is  about  40°,  and 
when  its  apparent  diameter  is  about  40",  and  about  £  of  the  entire 
disc  is  visible,  this  portion  giving  more  light  than  phases  of  greater 
extent,  because  the  latter  are  presented  at  so  much  greater  distances. 
During  every  eight  years,  when  the  planet  has  its  greatest  north  lati- 
tude and  is  40°  from  the  sun,  its  brilliancy  is  so  dazzling  that  it  is 
visible  in  full  daylight,  and  casts  a  sensible  shadow  in  the  evening. 
This  was  the  case  in  Feb.  1862,  and  had  been  often  observed  previously. 

220.  The  aphelion  distance  of  Venus  from  the  sun  is 
about  66,600,000;   the  perihelion  distance,  65,700,000;  its 
mean  distance  being  about  66,150,000. 

a.  The  mean  distance  can  be  calculated  by  Kepler's  third  law  ;  and 
the  aphelion  and  perihelion  distances  by  the  greatest  and  least  extreme 
elongations,  as  in  Art.  208. 


he  pupil  should  be  required  to  make  the  calculations  in  each 
case.  The  ratios  or  sines  of  the  angles  can  be  found  by  consulting  any 
ordinary  table  of  natural  sines.  The  term  natural  is  employed  to  distin- 
guish these  ratios  from  the  logarithmic  expression  of  them.] 

b.  The  absolute  eccentricity  of  Venus,  it  will  be  seen,  is  only  about 
450,000  miles,  or  less  than  .0069  of  its  mean  distance.  So  nearly  does 
the  orbit  resemble  a  circle. 

221.  The  apparent  diameter  of  Venus,  when  greatest,  is 
66^"  ;  and  when  least,  somewhat  less  than  10".  At  its 
mean  distance  (91  millions  of  miles)  from  the  earth  it  is 
about  17";  and  therefore  its  real  diameter  is  7510  miles. 
(Art.  210.)  The  compression  or  oblateness  of  the  planet 
is  exceedingly  small. 

a.  Volume,  Mass,  and  Density.  —  The  volume  of  Venus  is  about 
.85  of  the  earth's  ;  while  its  mass  is  .89  ;  hence  its  density  must  be 


QUESTIONS. — 219.  Extreme  elongation  ?  «.  Why  but  slightly  variable  ?  b.  When  is 
Venus  most  brilliant  ?  220.  Distances  of  Venus  ?  a.  How  calculated  ?  ft.  Eccentric- 
ity? 221.  Apparent  and  real  diameter  ?  a.  Volume,  mass,  and  density  ? 


VENUS.  159 

.89-^.85  =  1.047  (nearly),  or  very  Ifttle  greater  than   that   of   the 
earth. 

b.  Superficial  Gravity.— This  is  found  as  in  Art.  210,  e,  (f?gf)2  X 
.89  =  .98  ;  that  is,  a  pound  at  the  earth's  surface  would  weigh  only  .02 
less  at  the  surface  of  Venus. 

222.  The  diurnal  rotation  of  Venus  is  performed  in  23h 
21m  19s. 

«.  This  is  the  period  as  determined  by  Schroeter  in  1 789,  by  discov- 
ering a  luminous  point  in  the  dark  hemisphere  a  little  beyond  the 
southern  horn  of  the  planet,  indicating  the  existence  there  of  a  high 
mountain.  By  watching  its  periodic  changes,  he  was  enabled  to 
deduce  the  time  of  the  rotation ;  which  agreed  very  nearly  with  the 
result  attained  in  1667,  by  Cassini,  and  was  subsequently  confirmed 
by  the  observations  of  other  astronomers. 

b.  Mountains  in  Venus. — According  to  Schroeter,  there  exist  mount- 
ains of  immense  height  on  the  surface  of  Venus  ;  the  elevation  of  the 
loftiest  being  equal  to  T{v  of  the  planet's  radius,  which  would  be 
about  27  miles,  or  five  times  the  altitude  of  the  loftiest  terrestrial  peak. 

Fig.  93. 


TELESCOPIC   VIEWS   OF   VENtTS. 

While  other  astronomers  have  detected  the  existence  of  mountains  on 
the  planet,  their  observations  do  not  confirm  the  statements  of 
Schroeter  as  to  their  height.  Very  great  irregularities  on  its  sur- 
face are,  however,  indicated  by  the  jagged  character  of  the  termi. 
nator,  by  the  shading  of  its  edge,  and  by  the  blunt  or  broken 
extremities  of  its  cusps.  The  shading  is  supposed  to  be  caused  by  the 
long  shadows  cast  by  the  mountains  as  the  sun  shines  obliquely  upon 
them.  [See  Fig.  96.]  The  telescopic  observation  of  Venus  is  attended 

QUESTIONS. — b.  Superficial  gravity  ?    222.  Time  of  diurnal  rotation  ?    a.  How  deter, 
mined  ?    6.  Mountains  in  Venus  ?    What  indications  in  the  telescopic  views  ? 


160  .  VENUS. 

with  great  difficulty  on  account  of  the  intense  brilliancy  of  its  light, 
which  dazzles  the  eye  and  augments  all  the  imperfections  of  the 
instrument. 

223.  There  are  undoubted  indications  that  Yenus  is  sur- 
rounded by  an  atmosphere  of   considerable    height   and 
density. 

a.  This  is  shown  by  several  circumstances  :  1.  When  the  planet 
was  seen  as  a  narrow  crescent,  Schroeter  remarked  a  faint  light  pro- 
jecting beyond  the  proper  termination  of  one  of  the  horns  into  the 
dark  part  of  the  planet.  This  has  been  seen  by  other  observers,  and  is 
supposed  to  be  due  to  the  existence  of  an  atmosphere  refracting  the 
light  of  the  sun.  2.  By  observing  the  concave  edge  of  the  crescent,  it 
is  found  that  the  enlightened  part  does  not  terminate  suddenly,  but  that 
there  is  a  gradual  fading  away  of  the  light  into  the  dark  portion  of  the 
planet's  surface,  this  being  obviously  occasioned  by  a  reflection  of  the 
sun's  rays,  producing  the  phenomenon  of  twilight.  3.  During  the  tran- 
sits of  1761  and  1769,  the  planet  was  observed,  by  several  astronomers, 
to  be  surrounded  by  a  faint  ring  of  light,  caused,  as  it  has  been  sup- 
posed, by  the  sun's  rays  passing  through  the  planet's  atmosphere. 
4  Clouds  have  been  observed  floating  over  the  disc  of  the  planet,  and 
screening  by  their  greater  brilliancy  its  darker  surface,  which  is  occa- 
sionally seen  between  them.  Such  being  the  case,  there  must  be  water 
as  well  as  air  on  the  surface  of  Venus. 

224.  The  inclination  of  the  axis  of  Venus  has  not  been 
positively  ascertained ;  but  it  is  supposed  to  be  very  great, 
according  to  several  astronomers,  about  75°. 

a.  This  can  be  positively  discovered  only  by  observing  spots  on  the 
disc,  and  noticing  the  direction  of  their  apparent  motion.  This,  in  the 
case  of  Venus,  is  exceedingly  difficult,  owing  to  the  intense  brilliancy 
of  its  light  and  the  density  of  its  atmosphere.  Cassini,  as  early  as 
1666-7,  saw  one  bright  and  several  dusky  spots,  and  others  have  been 
observed  since  that  time  by  different  astronomers,  among  whom, 
De  Vico,  at  Rome,  in  1839-41,  appears  to  have  attained  the  most  reli- 
able results. 

QUESTIONS.— 223.  Has  Venus  any  atmosphere?  a.  What  indications  of  it?  224. 
Inclination  of  the  aris  of  Venus?  -a.  How  discorered? 


VENUS.  161 

225.  If  the  axis  of  Venus  has  an  inclination  of  75°,  its 
tropics  must  be  75°  from  its  equator,  and  its  polar  circles 
75°  from  the  poles.     Hence  it  can  have  only  a  torrid  zone, 
which  must  be  150°  wide,  and  frigid  zones  extending  75° 
from  the  poles. 

226.  SEASONS  OF  VENUS. — As  the  sun  must  arrive  at  the 
equator  and  depart  to  its  greatest  distance  from  it  twice  dur- 
ing each  sidereal  period,  there  must  be  two  summers  and 
two  winters  at  this  part  of  the  planet,  and  a  summer  and 
winter  at  each  of  the  poles,  which  must  suffer  a  transition 
from  the  burning  heat  of  a  vertical  sun  and  constant  day, 
to  the  intense  cold  of  perpetual  night,  each  lasting  more 
than  112  days. 

Fig.  97. 


Fig.  97  exibits  the  relative  positions  of  the  tropics  and  polar  circles,  the 
former  being  the  nearest  to  the  poles.  The  sun  is  represented  as  in  the 
northern  solstice ;  and  it  will  be  seen  that  all  places  situated  more  than  15° 
north  of  the  equator  have  constant  day,  and  those  more  than  15°  south  of 
it,  constant  night.  Hence  there  must  be  winter  at  the  equator  and  within 
the  south  polar  circle,  and  summer  within  the  north  polar  circle.  In 
one-fourth  of  the  year,  when  the  sun  will  have  arrived  at  the  equator, 
there  will  be  equal  day  and  night  all  over  the  planet,  summer  at  the  equa- 
tor, autumn  within  the  north  polar  circle,  and  spring  within  the  south  polar 
circle. 

Fig.  98  exhibits  the  planet  at  each  of  the  equinoxes  and  solstices :  To  an 
inhabitant  of  the  northern  hemisphere  of  Venus,  at  A  the  sun  is  in  the  vernal 
equinox ;  B,  the  summer  solstice  ;  C,  the  autumnal  equinox ;  and  D,  the 

QUESTIONS.— 226.  Zones  of  Venus  ?    22«.  Seasons  ?    Illustrate  by  the  diagram. 


162  VEKUS. 

winter  solstice.      To  an    inhabitant  of  the   southern  hemisphere,  these 
would,  of  course,  be  reversed. 

Fig.  98. 


SEASONS  OF  VENUS. 

227.  Venus  performs  its  sidereal  revolution  in  about  224f 
days  (224d  16h  49m) ;  its  synodic  period  is  about  584|  days. 

a.  For  its  sidereal  period  is  2247  days,  and  365.25-^224.7  =  If  ; 
hence  1 1  —  1  =  f ,  is  the  part  of  a  synodic  revolution  performed  in 
365i  days  ;  and  365i  -*-  f  =  584^  days.  [See  Art.  212,  a.] 

6.  Division  of  the  Synodic  Period. — Since  the  mean  value  of 
the  extreme  elongation  of  Venus  is  46°,  which  is  the  angle  M  E  S 
(Fig.  93),  the  angle  at  the  sun  M  S  E  must  be  90°  —  46°  =  44°.  There- 
fore the  planet,  in  passing  from  M  to  the  other  point  of  extreme 
elongation,  has  to  gain  on  the  earth  88° ;  and  the  time  required 
for  this  must  bear  the  same  ratio  to  584£  days  as  this  angle  bears  to 
360°.  Consequently,  the  synodic  period  is  divided  into  the  following 
intervals  :  /6fi0-  X  584£  days  =  142.9  days,  the  interval  between  the  time 
of  greatest  elongation  before  and  after  inferior  conjunction,  and  f^§ 
X  584^  days  =  441.1  days,  the  interval  between  the  elongation  before 
and  after  superior  conjunction.  One-half  of  each  of  these  intervals 
will  give  the  time  from  the  greatest  elongation  to  inferior  conjunction, 
and  that  from  greatest  elongation  to  superior  conjunction,  respectively. 

QUESTIONS. — 227.  Sidereal  period?  Synodic  period?  a.  How  calculated ?  6.  In- 
terval of  time  between  the  elongations  and  conjunctions? 


VENUS.  163 

c.  Morning  and  Evening  Star. — Since  Venus  must  remain  on 
each  side  of  the  sun  during  292  days,  or  one-half  the  synodic  period, 
it  must  be  a  morning  and  evening  star  alternately  for  that  time 

228.  The  distance  of  Venus  from  the  sun  being  a  little 
more  than  770  the  distance  of  the  earth,  the  apparent  diame- 
ter of  the  sun  must  be  1|  as  great,  or  about  45'.    Hence  the 
solar  light  and  heat  must  be  more  than  twice  as  great. 

a.  For  these  vary  inversely  as  the  squares  of  the  distances  ;  and  as 
the  ratio  of  the  distances  is  .723,  (,723)2,  or  about  .52  will  be  the  ratio 
of  the  light  and  heat  of  the  earth  to  those  of  Venus.  This,  of  course, 
may  be  very  much  modified  by  the  influence  of  its  atmosphere. 

229.  TRANSITS  or  VENUS. — The  orbit  of  Venus  is  in- 
clined to  the  ecliptic  at  an  angle  of  3J°  (3°  23'  29") ;  and 
therefore  a  transit  can  take  place  only  when  the  planet  is  at 
or  near  one  of  its  nodes.      The  transits  of  Venus  are  of 
great  interest  and  importance,  because  they  afford  a  means 
of  determining  the  parallax  of  the  sun,  and  consequently  its 
distance  from  the  earth. 

a.  History  of  Transit  Observations.— These  transits  are  of  rare 
occurrence.  Kepler,  in  1629,  predicted  that  a  transit  would  occur  in 
1631,  and  that  no  other  would  occur  until  1761.  His  prediction,  how- 
ever, was  not  confirmed  by  observation,  for  the  transit  of  1631 
occurred  during  the  night ;  and  in  1639  the  first  observation  of  a 
transit  was  made  by  a  young  English  astronomer,  named  Horrox.  No 
other  occurred  till  1761  and  1769  ;  and  these  were  observed  with  great 
care  in  different  parts  of  the  world,  in  order  to  apply  the  method  of 
finding  the  solar  parallax,  first  suggested  by  Gregory,  a  celebrated 
mathematician,  in  1663.  King  George  III.,  in  1769,  despatched,  at  his 
own  expense,  an  expedition  to  Otaheite,  under  the  command  of  the 
celebrated  navigator,  Captain  Cook,  in  order  that  observations  of  the 
transit  might  be  taken  in  this  distant  spot.  Other  nations  sent  in  dif- 
ferent directions  similar  expeditions.  The  average  result  of  these 
different  observations  assigned  as  the  true  solar  parallax  8.5776",  which 

QUESTIONS.—*.  How  long  does  Venus  remain  a  morning  or  evening  star?  228. 
Solar  light  and  heat  at  Venus?  a.  Why?  229.  When  do  transits  occur?  Why  im- 
portant? a.  History  of  transit  observations? 


164  VEKUS, 

has,  within  a  very  few  years,  been  found  to  be  somewhat  too  small. 
The  next  transit  will  occur  in  1874. 

b.  Times  of  the  Occurrence  of  Transits.-— The  longitudes  of  the 
nodes  of  Venus  are  about  75°  (ft),  and  255°  ("tf ) :  hence,  they  are  in 
the  15th  degree  of  Gemini  and  Sagittarius ;  and  as,  therefore,  the  earth 
arrives  at  the  line  of  nodes  early  in  June  and  December,  the  transits 
must  occur  in  these  months  ,  and  will  continue  to  do  so  for  a  long  time, 
since  the  longitude  of  the  nodes  diminishes,  according  to  Le  Verrier,  at 
the  rate  of  less  than  18'  in  a  century. 

c.  Because  8  sidereal  periods  of  the  earth  are  very  nearly  equal  to 
13  of  Venus,  transits  often  occur  at  intervals  of  eight  years ;  when, 
however,  two  transits  have  occurred  at  this  interval,  another  can  not 
be  expected  before  105^  years.     Thus,  the  next  transit  will  happen  in 
December,  1874  ;  and  another  in  1874  +  8  =  1882  (December  6th).    The 
next  will  not  occur  till  June  7th,  2004,  121£  years  afterwards.     The 
transits  are  thus  repeated  at  intervals  of  8,  105i  8,  121i  8  years,  etc. ; 
acccording  as  they  occur  at  one  or  the  other  node. 

d.  How  to  Find  the  Sun's  Parallax  by  the  Transits  of  Venus. 

By  the  greatest  elongation,  the  distance  of  an  inferior  planet  from  the 
aun  can  be  found,  provided  we  know  the  earth's  distance.     We,  in  fact, 
only  find  by  this  method  the  ratio  of  one  distance  to  the  other ;  and 
this  is  known,  therefore,  independently  of  the  solar  parallax. 


Fig,  99. 


TRANSIT  OF  VENUS. 

In  Fig.  99,  let  A  and  B  be  the  positions  of  two  observers  stationed  at  op- 
posite parts  of  the  earth,  and  V,  the  place  of  Venus  at  the  time  of  a  transit. 
The  observer  at  A  will  see  the  planet  projected  on  the  sun  at  a,  and  the 
observer  at  B,  at  6 ;  and  if  each  observer  notice  exactly  the  time  required 

QUKBTIONS. — 6.  Which  are  the  node  months  ?  Why  ?  c.  Epochs  of  the  occurrence 
of  transits  ?  d.  How  is  the  solar  parallax  found  by  transit  observations? 


VENUS.  165 

by  the  planet  to  cross  the  disc,  he  can,  since  its  hourly  motion  is  known, 
easily  calculate  the  length  of  the  chord  which  it  appears  to  describe  at  each 
place  ;  and  a  comparison  of  the  length  of  these  chords  will  give  the  dis- 
tance between  a  and  b  in  seconds  of  space.  Now,  if  Venus  were  exactly 
half-way  between  the  earth  and  sun  the  distance  a  &  as  seen  from  the  earth 
would  be  exactly  the  same  as  A  B  seen  from  the  sun ;  and  therefore  would  be 
twice  the  parallax.  But  the  distance  of  Venus  from  the  sun  is  known  to 
be  .723  of  the  earth's  distance;  and  consequently  AV,  its  distance  from 
the  earth,  must  be  1  —.723  =  .277  ;  so  that  the  ratio  of  a  V  to  A  V  is  £?f  =  2.6 
(nearly).  But  a  b  bears  the  same  ratio  to  A  B  as  a  V  does  to  A  V  :  hence, 
the  distance  a  b  must  be  2.6  x  2  or  5.2  times  the  solar  parallax.  Suppose, 
therefore,  this  distance  should  be  found  by  observation  and  calculation  to 
be  46k"  ;  then  46|"  -»-  5.2  =  8.94"  would  be  the  true  parallax.  The  advan- 
tage afforded  by  this  method  is,  that  because  the  distance  of  Venus  from  the 
earth  is  so  much  less  than  from  the  sun,  a  b  is  enlarged  in  the  same  pro- 
portion, and  thus  rendered  motjfc  susceptible  of  exact  measurement.  Thus, 
it  will  be  obvious  that  whateverrerror  arises  in  determining  a  &,  affects  the 
parallax  less  than  one-fifth.  Practically,  it  is  impossible  that  the  observers 
should  be  as  far  apart  as  A  B  ;  but  whatevejtheir  distance  from  each  other, 
it  can  be  easily  reduced  to  the  conditionsfa'epresented  in  the  diagram. 

APPARENT  MOTIONS  OF  THE  INFERIOR  PLANETS. 

230.  The  APPAKENT  MOTIONS  of  Mercury  and  Venus  are 
sometimes  from  west  to  east,  and  sometimes  from  east  to 
west.  The  former  are  said  to  be  direct ;  the  latter,  retro- 
grade. At  certain  intermediate  points,  the  planet  appears 
to  remain  for  a  short  time  in  the  same  point  of  the  heavens, 
and  is  then  said  to  be  stationary. 

a.  The  student  must  clearly  understand  that  these  motions  and 
stationary  points  have  reference  to  the  stars,  not  to  the  sun  ;  the  appa- 
rent place  of  the  latter  is  constantly  changing  on  account  of  the 
motion  of  the  earth.  These  phenomena  are  illustrated  in  the  annexed 
diagram. 

Let  S  (Fig.  100),  be  the  place  of  the  sun,  the  inner  circle  the  orbit  of  an 
inferior  planet ;  the  outer  circle  that  of  the  earth.  Let  also  a,  6,  c,  d,  etc., 
be  the  positions  of  the  planet  at  unequal  intervals  of  time  between  the  points 

QTTESTIONS. — 230.  What  apparent  motions  have  Mercury  and  Venus  ?  When  are 
they  said  to  be  stationary  ?  a.  Does  this  refer  to  the  Bun  or  the  stars?  Explain  tha 
,  phenomena  from  the  diagram. 


166 


VENUS. 


of  extreme  elongation,  a  and  g ;  and  A,  B,  C,  D,  etc.,  the  places  of  the 
earth  at  the  same  time;  while  1,  2,  3,  4,  etc.,  represent  the  apparent  places 
of  the  planet,  as  seen  in  the  sphere  of  the  heavens.  In  passing  from  g, 
the  western  point  of  extreme  elongation,  through  o,  the  place  of  superior 

Fig.  100. 


APPABENT  MOTIONS  OF  VENUS  AND   MEHCT7BY. 

conjunction,  to  a,  the  eastern  point  of  extreme  elongation,  the  planet  evi- 
dently must  appear  to  move  toward  the  east ;  and  when  it  arrives  at  a,  the 
earth  being  at  A,  it  still  continues  to  be  direct  for  a  short  time ;  for  while 
going  from  a  to  &  its  motion  is  so  oblique  that  the  earth  passes  it,  so  that 
when  the  latter  arrives  at  B,  the  planet  appears  to  have  moved  from  1  to  2. 
Its  elongation  is  not,  however,  increased  since  the  sun  itself  has  moved  far- 
ther to  the  east.  While  the  planet  is  going  from  &  to  c,  and  the  earth  from 
B  to  C,  the  former  does  not  appear  to  change  its  position  at  ail ;  for  the 
lines  B  &  2  and  C  c  3  are  parallel,  and  consequently  indicate  no  change  of  place 
among  the  stars,  and  2  is  to  be  considered,  therefore,  as  identical  with  3. 
The  reason  of  the  planet's  appearing  stationary,  it  will  be  seen,  is  that  the 
obliquity  of  its  motion  exactly  counterbalances  the  difference  between  its 
actual  velocity  and  that  of  the  earth ;  I  is,  therefore,  to  be  considered  the 
stationary  point.  At  d,  the  planet  is  in  inferior  conjunction,  having  overtaken 
the  earth,  and  is  seen  at  4,  to  the  west  of  its  previous  position.  In  passing 


VENUS.  167 

from  d  to  g  the  same  phenomena  are  presented  in  the  reverse  order ;  at  e  it 
becomes  stationary,  remaining  so  till  it  reaches  /,  where  it  ceases  to  he  ret- 
rograde, appearing  to  move  while  going  from  /to  g,  from  6  to  7.  In  going 
from  c  to  e,  the  two  stationary  points,  it  has  evidently  changed  its  direction 
among  the  stars,  not  by  the  actual  distance  3, 5,  but  by  the  angle  contained  by 
the  lines  3  c  C  and  5  e  E  when  produced  until  they  meet  in  some  point  be- 
low C  D  E.  This  angle,  or  the  arc  by  which  it  is  subtended,  it  is  obvious,  is 
quite  small ;  it  is  called  the  arc  of  retrogradation.  From  the  above  ex- 
planation the  following  statements  will  be  understood. 

231.  An  inferior  planet  appears  stationary  at  two  points 
of  its  synodic  revolution,  between  the  extreme  elongations 
and  inferior  conjunction.  Its  motion  is  retrograde  in 
passing  through  inferior  conjunction  from  one  stationary 
point  to  the  other ;  and  direct  in  passing  through  superior 
conjunction,  between  the  same  two  points. 

a.  The  stationary  points  of  Mercury  vary  from  15°  to  20°  of  elonga- 
tion from  the  sun  ;  those  of  Venus  generally  occur  when  its  elongation 
is  about  29°.  (See  Fig.  95). 

ft.  The  time  during  which  Mercury  retrogrades  is  about  22  days; 
Venus,  42  days.  The  mean  arc  of  retrogradation  of  the  former  is  about 
12±° ;  of  the  latter,  16°.  The  stations  of  both  are,  of  course,  but  of 
very  short  duration. 

QUESTIONS.— 231.  When  does  an  inferior  planet  appear  stationary?  When  is  its 
motion  direct  ?  When,  retrograde  ?  a.  Where  are  the  stations  of  Mercury  and  Venus  ? 
6.  During  how  many  days  does  each  retrograde  ?  How  long  are  the  arcs  of  retrogra- 
dation? 


CHAPTER   XIII. 

THE    SUPERIOR    PLANETS. 
I.  MARS.      $ 

232.  MARS,  the  fourth  planet  from  the  sun  (the  most 
distant  of  the  terrestrial  planets),  is  remarkable  for  its  small 
size  and  the  red  color  with  which  it  shines  among  the  stars. 

a.  Name  and  Sign. — This  redness  of  its  appearance  makes  it  easily 
distinguished  among  the  other  heavenly  bodies,  and  doubtless  gave 
rise  to  its  name ;  Mars,  in  the  heathen  mythology,  being  the  god  of 
war.  Its  sign  is  a  shield  and  spear. 

233.  PHASES. — When  Mars  is  in  opposition  or  conjunc- 
tion, its  disc  is  full ;  when  between  these  points,  it  is  gibbous. 
More  than  half  of  its  disc  is,  therefore,  always  visible. 

a.  The  reason  of  this  will  be  apparent  after  a  little  consideration. 
In  opposition  and  conjunction,  the  hemisphere  presented  to  the  earth 
exactly  coincides  with  the  illuminated  disc ;  hence,  the  planet  appears 
full.  The  amount  of  diminution  of  the  full  disc  is  obviously  equal  to 
the  angle  formed  at  the  centre  of  the  planet  by  lines  drawn  to  the 
earth  and  sun.  (See  Fig.  75.)  As,  in  the  case  of  a  superior  planet,  this 
angle  is  always  less  than  a  right  angle,  the  amount  of  dimunition 
must  be  less  than  one-half  of  the  disc  ;  for  a  right  angle  would  include 
one-quarter  of  the  whole  surface,  which  is,  of  course,  one-half  of  the 
disc.  Therefore,  the  planet  can  present  no  other  than  the  full  or 
gibbous  phase. 

234.  The  APPARENT  MOTIONS  of  a  superior  planet,  like 

QUESTIONS.— 232.  For  what  is  Mars  remarkable?  a.  Name  and  sign?  233.  What 
phases  does  it  exhibit?  a.  How  is  this  explained ?  234.  What  apparent  motions  have 
the  superior  planets  ? 


MARS.  1C9 

those  of  an  inferior  planet,  are  either  direct  or  retrograde ; 
and  as  its  motion  changes  from  one  to  the  other,  it  appears 
for  a  short  time  to  be  stationary. 

235.  The  motion  appears  to  be  retrograde  for  a  short  dis- 
tance before  and  after  opposition,  and  direct  in  the  other 
part  of  its  orbit.      The  retrogradation   of  the  planet  is 
caused  by  the  greater  velocity  of  the  earth  ;  so  that  as  the 
latter  body  moves  toward  the  east,  it  passes  the  other,  and 
thus  makes  it  appear  to  move  toward  the  west.    When  the 
motion  of  the  earth  is  sufficiently  oblique  to  counteract  the 
excess  of  its  velocity,  the  two  bodies  move  on  together,  and 
the  planet  appears  to  be  stationary. 

a.  The  arc  of  retrogradation  in  the  case  of  the  superior  planets 
is  very  small.     The  following  is  the  mean  value  of  each  :  Mars,  15° ; 
Jupiter,  10' ;  Saturn,  6J° ;  Uranus,  3|° ;  Neptune,  about  2°. 

b.  Mars  retrogrades  from  60  to  80  days,  according  as  it  is  in  perihe- 
lion or  aphelion;    Jupiter  continues  to  retrograde  during  about  4 
months ;  Saturn,  about  4^  months ;  Uranus,  about  5  months  ;  Neptune 
about  6  months. 

c.  Mars  becomes  stationary  when   its  elongation  is  about  140°  ; 
Jupiter,  115° ;  Saturn,  110° ;  Uranus,  103° ;  Neptune,  97£°. 

236.  The  aphelion  distance  of  Mars  is  about  152,300,000 
miles  ;  its  perihelion  distance,  126,300,000 ;  hence,  its  mean 
distance  is  about  139,300,000. 

a.  Since  the  periodic  time  of  Mars  is  1^  322d ,  we  have,  by  Kepler's 
third  law,  (365J)2:(687i)2 :  :(91,500,000)3:  the  cube  of  the  distance  of 
Mars,  which,  by  working  out  the  proportion,  will  give  very  nearly  the 
mean  distance  above  stated. 

b.  The  distance  can  also  be  found  approximately  by  observing  the 
phase  of  Mars  when  it  varies  most  from  the  full.     The  following  is  the 
method : — 

Let  S  (Fig.  101),  represent  the  sun,  E,  the  earth,  and  M,  Mars,  much 

QUESTIONS.— 235.  When  is  the  motion  retrograde?  Why  ?  When  is  the  planet  sta- 
tionary ?  Why?  a.  What  is  the  arc  of  retrogradation  of  each  superior  planet ?  b. 
How  long  does  each  retrograde?  c.  Where  are  the  stationary  points?  236.  Distance 
of  Mars  from  the  sun  ?  a.  How  found  by  Kepler's  third  law  ?  b.  How  by  the  phase  ? 


170 


MARS. 


Fig.  101  enlarged  for  convenience  of  illustra- 

tion. The  earth  is  obviously  at  the 
point  of  greatest  elongation  as  seen 
from  Mars ;  and  hence  the  angle 
S M  E  is  the  largest  possible.  But  this 
is  equal  to  a  M  d  which  measures  the 
deviation  of  the  disc  from  the  full; 
for  the  arc  b  a  =  e  d  ;  and  taking  e  a 
from  each,  there  remain  be  =  ad.  Sup- 
pose this  angle  is  measured  and  found 
to  be  41°  4'.  Then  the  sine  of  this  angle 
being  about  .657,  this  must  be  the 
ratio  of  the  distance  of  the  earth  to 
/  that  of  Mars  ;  and  91,500,000  -*-  .657  = 

139,300,000  (nearly).      This  method  is 
applicable   only  to    Mars;    since    the 

other  planets  are  so  far  distant  that  the  angle  of  elongation  corresponding 
to  S  M  E,  is  very  small ;  and  their  deviation  from  the  circular  outline  not 
large  enough  to  be  susceptible  of  exact  measurement. 

c.  A  more  general  method,  based  upon  the  daily  arc  of  retrograda- 
tion  of  the  superior  planets,  is  interesting  as  having  been  employed 
by  the  old  astronomers,  and  more  particularly  by  Kepler  in  those 
investigations  which  resulted  in  the  discovery  of  his  third  law.  The 
following  is  a  brief  statement  of  this  method : — 

Let  S  (Fig.  102),  represent  the  sun,  E  t  the  daily  arc  of  movement  of  the 
earth,  and  M  m,  that  of  Mars  in  opposition.  In  going  from  M  to  w,  the 
planet  obviously  changes  its  direction  backward  among  the  stars  by  the 
angle  d  e  o  =  e  o  E.  Now,  in  the  triangle  o  e  S,  the  angle  o  is  given,  also  the 

Fig.  102. 


angle  E  S  c,  since  it  is  the  amount  of  angular  movement  of  the  earth 
for  the  time ;  hence,  the  third  angle  o  eS  becomes  known ;  and  the  ratio  of 
o  S  to  c  S,  since  this  is  equal  to  the  ratio  of  the  sines  of  o  eS  and  e  08.  In 
the  triangle  o  m  S  we  have,  in  the  same  manner,  the  angles  o  and  m  S  M, 
the  latter  being  the  angular  movement  of  the  planet,  so  that  the  ratio  of 


QUESTION. — c.  How  may  the  distance  be  found  by  the  arc  of  retrogradation  ? 


MARS.  171 

o  S  to  m  S  becomes  known ;  whence,  combining  the  two  results,  we  obtain 
the  ratio  of  m  S  to  e  S,  or  that  of  the  two  distances ;  on  the  supposition, 
however,  that  the  orbits  are  circular ;  but  when  the  process  is  repeated  in 
every  variety  of  situation  at  which  the  opposition  may  occur,  the  average 
of  the  results  will  give  a  tolerably  accurate  determination. 

237.  The  ECCENTRICITY  of  the  orbit  of  Mars  is  about  13 
millions  of  miles,  or  .093  of  its  mean  distance.  It  is,  there- 
fore, nearly  5]  times  as  great  as  that  of  the  earth. 

a.  Parallax  of  Mars  and  of  the  Sun.— Owing  to  the  great  eccen- 
tricity of  the  orbit  of  Mars,  it  sometimes,  when  in  opposition,  approaches 
very  near  to  the  earth  ;  for  if  it  is  in  perihelion  while  the  earth  is  in 
aphelion,  the  distance  is  126,300,000—93,000,000  =  33,300,000.  Ad- 
vantage was  taken  of  this  in  1862  to  determine  its  parallax.  It  was 
arranged  that  several  observers  should  station  themselves  at  places  in 
different  hemispheres  and  record  the  zenith  distance  of  the  planet 
when  on  the  meridian,  as  well  as  its  distance  from  certain  stars,  so  as 
to  ascertain  the  amount  of  displacement  in  its  position  occasioned  by 
the  separation  of  the  observers.  These  observations  were  made  at 
Greenwich,  Pulkova,  Washington,  Cape  of  Good  Hope,  Williamstown 
in  Australia,  and  Santiago. 

An  effort  was  also  made  to  determine  the  parallax  at  a  single  obser- 
vatory, by  observing  the  displacement  in  the  apparent  position  of  the 
body,  occasioned  by  the  rotation  of  the  earth.  For  as  the  observer  is 
not  situated  at  the  centre  of  motion,  the  planet  can  only  appear  pre- 
cisely in  its  true  place,  as  to  right  ascension,  When  it  is  on  the  meridian  ; 
and  frequent  observations  made  before  and  after  culmination  must 
show  an  average  displacement,  from  which  its  parallax  may  be  calcu- 
lated, and  consequently  its  distance  from  the  earth.  From  this  may 
be  deduced  the  earth's  distance  from  the  sun,  and  of  course  the  solar 
parallax.  The  results  of  the  different  observations  very  nearly  agreed, 
all  showing  the  parallax  as  determined  in  1769  to  be  too  small.  The 
average  result  is  that  now  generally  accepted  (8.94").  Le  Verrier  had 
previously  assigned  very  nearly  the  same  amount  by  calculations  based 
upon  the  disturbances  of  the  planets,  which  showed  that  the  parallax 
needed  correction  in  order  to  bring  the  observed  perturbations  into 
harmony  with  those  theoretically  computed. 

QUESTIONS. —237.  What  is  the  eccentricity  of  the  Ofbit  of  Mars?    a.  Hotir  to  find  the 
parallax  of  Mars,  and  the  solar  parallax? 


172  MAES. 

238.  The  INCLINATION  OF  THE  ORBIT  of  Mars  to  the  plane 
of  the  ecliptic  is  only  about  two  degrees  (1°  51'). 

239.  Its  SIDEEEAL  PERIOD  is  nearly  687  days ;  its  synodic 
period,  780  days. 

a.  For  687d—  365id=321^  ;  hence,  687*  -4-  321  ^  =  2.135,  is  the 
number  of  revolutions  of  the  earth  during  the  synodic  period;  and 
365  $d  X  2.135  =  780d  (nearly).  In  Art.  62,  the  same  method  is  applied 
fractionally  ;  thus,  365id  =  .532  of  687d;  hence,  the  earth  gains  in  one 
revolution  1  —  .532  =  .468  of  a  revolution  upon  the  planet ;  but  she 
has  to  gain  an  entire  revolution  ;  and  1  -r-  .468  —  2.135  revolutions 
(nearly). 

240.  The  apparent  diameter  of  Mars  varies  between  4"  in 
conjunction  and  30"  in  opposition.      Its  real  diameter  is 
about  4,300  miles.     Its  oblateness  is  about  5-'0  of  its  diame- 
ter, or  86  miles,  and  is  consequently  very  nearly  six  times  as 
great  as  the  earth's. 

241.  It  performs  its  daily  rotation  in  about  24  J  hours 
(24h  37m  42s),  upon  an  axis  inclined  toward  its  orbit  28°  42' ; 
hence  its  obliquity  is  nearly  the  same  as  the  earth's,  and  its 
variety  of  seasons  also  the  same,  except  that  they  are  nearly 
twice  as  long. 

a.  Seasons  of  Mars.— The  year  of  Mars  contains  668J  16h  of  its 
own  time,  since  its  days  are  longer  than  those  of  the  earth.  Owing 
to  the  great  eccentricity  of  its  orbit,  summer  in  the  northern  hemi- 
sphere is  only  about  £  as  long  as  in  the  southern  ;  but  in  consequence 
of  its  greater  proximity  to  the  sun,  the  light  and  heat  are  much 
greater  (in  the  ratio  of  145  to  100).  Thus  there  is  a  complete  compen- 
sation in  the  seasons  of  both  hemispheres.  Constant  day  at  the  north 
pole  of  Mars  lasts  during  297  of  its  days ;  at  the  south  pole,  during 
372  days.  Hence,  constant  night  at  the  north  pole  is  75  days  longer 
than  at  the  south  pole. 

242.  The   TELESCOPIC    APPEARANCES  of  Mars  are  very 

QUESTIONS. — 238.  Inclination  of  its  orbit?  239.  The  sidereal  and  synodic  periods? 
*.  How  deduced?  240.  Apparent  diameter?  Real  diameter?  Oblateness?  241. 
Period  of  rotation  ?  a.  Seasons  ?  242.  Telescopic  appearances  of  Mars  ? 


MARS. 


173 


interesting,  exhibiting  what  seem  to  be  the  outlines  of 
continents  and  seas,  the  former  appearing  of  a  ruddy  or 
orange  color,  and  the  latter  of  a  dusky  greenish  or  bluish 
tint. 

243.  Brilliant  white  spots  are  also  seen  alternately  at  the 
poles,  produced,  as  it  is  conjectured,  by  accumulations  of 
ice  and  snow  during  the  long  winters,  particularly  as  they 
are  seen  to  disappear  as  summer  advances  upon  the  poles. 

244.  Evidences  are  also  presented  of  an  atmosphere,  prob- 
ably of  a  density  about  equal  to  that  of  the  earth. 

Fig.  1O3. 


NORTHERN   AND  SOUTHERN   HEMISPHERES  OP  MARS.  — 


a.  With  the  exception  of  the  moon,  no  body  has  been  submitted  to 
such  a  careful  telescopic  scrutiny  PS  Mars.  The  utmost  assiduity  has 
been  exercised  particularly  by  Messrs.  Beer  and  Madler  in  these 
researches,  which  were  commenced  by  them  in  1830,  and  continued 
at  every  opportunity  for  twe've  years.  A  large  collection  of  draw- 
ings of  the  various  hemispheres  presented  by  the  planet  was  made 
by  them,  showing  the  positions  and  outlines  of  the  spots  seen  on 
the  disc,  and  clearly  establishing  their  connection  with  the  planet's 


QUESTIONS.— 243.  The  white  spots  ?    244.  Atmosphere?    a.  Observations  of  Mars ? 


174  JUPITEK. 

surface,  and  their  general  permanency.  Considerable  variety  is,  how- 
ever, exhibited  in  the  forms  of  these  spots,  owing  to  the  great  diversity 
in  the  hemispheres  presented. 

The  annexed  cut  does  not  represent  any  actual  telescopic  views  of  the 
planet,  since  we  are  never  so  situated  as  to  be  able  to  see  the  whole  of  either 
the  northern  or  southern  hemisphere  at  any  one  time.  It  exhibits  a  combi- 
nation of  a  large  number  of  telescopic  appearances,  the  various  dusky  spots 
being  placed  tpgether  so  as  to  show  the  forms  of  the  different  bodies  of  water 
and  their  relation  to  the  continents ;  the  latter  being  indicated  by  the  white 
spaces.  These,  through  the  telescope,  appear  of  a  ruddy  color,  and  give 
this  general  tint  to  the  planet.  On  the  earth,  the  continents  are  islands, 
being  encompassed  by  the  water ;  on  Mars,  it  will  be  perceived,  the  bodies 
of  water  are  lakes  or  seas,  being  entirely  encompassed  by  the  land. 

6.  No  entirely  satisfactory  cause  has  been  assigned  for  the  ruddy 
color  of  this  planet.  It  is  thought  by  Sir  John  Herschel  to  be  due  to 
"  an  ochrey  tinge  in  the  general  soil,  like  what  the  red  sandstone  dis- 
tricts on  the  earth  may  possibly  offer  to  the  inhabitants  of  Mars, 
only  more  decided."  Viewed  through  a  telescope,  the  redness  of  its 
hue  is  very  considerably  diminished. 

II.   JUPITER      "$ 

245.  JUPITEK,  the  first  of  the  major  planets,  is  remakable 
for  its  great  size,  it  being  the  largest  of  all  the  planets. 
It  is  also  distinguished  for  the  peculiar  splendor  with  which 
it  shines  among  the  stars. 

a.  Name  and  Sign. — This  planet  doubtless  received  its  name  on 
account  of  its  superior  magnitude  and  splendor,  Jupiter,  or  Jove,  in  the 
ancient  mythology,  being  the  king  of  the  gods.  Its  sign  is  supposed 
to  be  an  altered  Z,  the  first  letter  of  Zeus,  the  name  of  Jupiter  among 
the  Greeks. 

246.  The    aphelion    distance  of  Jupiter  is    498,500,000 
miles ;  its  perihelion  distance  453,000,000  miles ;  hence  its 
mean  distance  is  475,750,000. 

247.  The  ECCENTRICITY  of  its  orbit  is  therefore  22,750,- 

QUESTIOXS.— &.  Cause  of  its  red  color?  245.  How  is  Jupiter  distinguished?  a, 
Name  and  sign  ?  246.  Distance  from  the  sun  f  247.  Eccentricity  ? 


JUPITER.  175 

000  miles,  or  about  .048  of   its    mean    distance ;    being 
relatively  nearly  three  times  that  of  the  earth. 

248.  The  inclination  of  its  orbit  is  very  small,  being  only 
about  1°  19'. 

249.  Its  SYNODIC  PERIOD  is  found  by  observation  to  be 
about  399  days ;  hence  its  SIDEREAL  PERIOD  is  about  4332 
days,  or  lly  315d. 

a.  For  399J -^  365  id=  1.0921  revolution  performed  by  the  earth 
during  the  synodic  period  ;  hence,  Jupiter  performs  only  .0921  of  a 
revolution  in  399*  ;  and  399d^-  .0921  =  4332«»+. 

250.  The  APPARENT  DIAMETER  of  Jupiter  in  opposition, 
when  greatest,  is  about  50" ;  in  conjunction,  31"  ;  and  at 
its  mean  distance  is  about  37".    Its  real  equatorial  diame- 
ter is  about  87,500  miles. 

a.  For  the  least  distance  of  Jupiter  from  the  earth  is  453,000,000— 
93,000,000  =  360,000,000  mile  ;  and  the  maximum  apparent  semi-diam- 
eter is  25",  the  sine  of  which  is  .0001215,  and  360,000,000  X  .0001215 
=  43,750  miles,  which  is  the  greatest,  or  equatorial,  semi-diameter. 
Hence  the  diameter  is  87,500  miles. 

251.  The  OBLATENESS  of  Jupiter  is  very  great,  being 
about  j\  cf  its  mean  diameter,  or  about  £,000  miles. 

a.  Its  polar  diameter  is  therefore  about  82,500  miles,  and  its  mean 
diameter  85,OOG  miles.     This  remarkable  degree  of  ellipticity  in  its 
figure  is  caused  by  the  rapid  rotation  on  its  axis,  which  is  performed 
in  a  little  less  than  10  hours  C9b  55  ^m) ;  BO  that  a  point  on  the  equator 
of  this  planet  moves  with  a  diurnal  velocity  of  nearly  28,000  miles  an 
hour,  or  27  times  as  fast  as  at  the  earth. 

b.  It  has  already  been  explained  (129  a)  that  the  oblateness  of  a 
planet's  figure  results  from  the  action  of  the  centrifugal  force  ;  and  it 
will  be  obvious  that  the  degree  of  oblateness  must  depend  on  the 
velocity  of  rotation  and  the  density  of  the  body.    It,  in  fact,  varies 
directly  as  the  square  of  the  former,  and  inversely  as  the  density,  or 

QUESTIONS — °4S.  Inclination  of  itg  orbit  ?  249.  Its  synodic  and  sidereal  periods  ? 
260.  Apparent  and  real  diameters?  a.  How  found?  251.  Ohlateness?  a.  Equatorial 
and  polar  diameters ?  Period  of  rotation ?  Velocity?  6.  How  to  tiud  the  oblatene«s 
from  the  velocity  ? 


176  JUPITER. 

the  attraction  of  the  body  on  its  own  matter.  Thus,  the  velocity  of 
Jupiter  is  about  2 §•  times  as  great  as  the  earth's  [24h  -5-  10h  =  2f],  but 
its  density  is  only  J  as  great,  and  (2 1)2  X  4  =  23  +.  Therefore,  if  its 
density  were  as  uniform  as  that  of  the  earth,  its  oblateness  would 
be  2^9  X  23  ==  i1;,  of  its  diameter.  The  internal  parts  of  Jupiter  must 
therefore  be  very  much  more  dense  than  the  external,  the  latter  prob- 
ably being  considerably  lighter  than  water. 

Fig.  1O4.  Ct  Volume,  Mass,  and 

Superficial  Gravity. — 
The  volume  of.  Jupiter  is 
about  1244  times  as  great 
as  the  earth's  ;  for  85,000 
-^7912  =  10. 75,  and 
(10.75)3  =  1244  (nearly). 

Its  mass  being  only  301, 
....  __. 

its  density  is  oOl  -r- 

1244  =  .242,  or  nearly  \. 
The  force  of  gravity  at 
the  surface  of  the  planet 
must  therefore  be  301  -J- 
(10.75)*  =  2.6+.  So  that 

COM  PABATIVE  MAGNITUDES  OF  TOE  BAKTH  AND  JUPITER.       a  body  Weighing    lib    at 

the  earth's  surface  would  weigh  2.6  Ibs  at  Jupiter's;  and  since  a 
body  falls  through  16  feet  in  the  first  second  of  time  at  the  earth's 
surface,  it  would  fall  more  than  41  feet  at  that  of  Jupiter. 

d.  Orbital  Velocity. — This  body,  so  inconceivably  vast,  is  flying  in 
its  orbit  with  the  velocity  of  28,700  miles  an  hour,  or  nearly  500  miles 
a  minute — a  speed  sixty  times  a  great  as  that  of  a  cannon  ball.  How 
tremendous  is  the  exhibition  of  force  here  displayed  1 

252.  The  inclination  of  Jupiter's  axis  to  that  of  its  orbit 
is  only  3°  (3°  6'),  much  too  small  to  cause  any  considerable 
change  of  seasons. 

a.  The  phenomena  of  constant  day  and  night  take  place,  therefore, 
only  within  two  small  circles  extending  3°  from  the  poles.  Exactly  at 
the  poles,  the  dey  and  night  are  alternately  about  six  years  long.  The 
cold  at  these  parts  of  Jupiter  must  be  intense  beyond  any  that  we  can 

^TTCSTIONS.— e.  Volume,  mass,  and  superficial  gravity?  d.  Orbital  velocity  ?  262 
Inclination  of  its  axis?  a.  What  results  from  this? 


JUPITER.  177 

conceive.  The  long  absence  of  the  sun,  and  its  never  rising  more 
than  3°  above  the  horizon,  joined  with  the  immense  distance  of  the 
planet  from  that  luminary,  must  all  combine  to  intensify  this  rigor. 

6.  Solar  Light  and  Heat. — The  light  and  heat  of  the  sun  at  Jupi- 
t3r  must  be  less  than  at  the  earth,  in  the  inverse  ratio  of  (475,500,000)2 
to  (90,000,000)2,  or  of  27  to  1.  This  feeble  supply  of  light  and  heat 
may,  however,  be  compensated  by  a  greater  density  of  the  atmosphere, 
a  higher  calorific  or  luminous  capacity  of  the  soil,  or  a  greater  amount 
of  internal  heat  than  that  possessed  by  the  earth. 

253.  BELTS  OF  JUPITER. — When  examined  with  a  tele- 
scope the  disc  of  Jupiter  appears  crossed  by  dusky  streaks 
or  belts,  parallel  to  its  equator,  their  general  direction  always 
remaining  the  same,  although  they  constantly  vary  in  num- 
ber, breadth,  and  situation  on  the  disc.   Sometimes  the  disc  is 
almost  covered  with  them ;  while  at  others  scarcely  any  are 
visible. 

254.  These  dusky  bands  or  belts  are  supposed  to  be  the 
body  of  the  planet  seen  between  the  clouds  that  constantly 
float  in  its  atmosphere,  and  are  thrown  into  zones  or  belts  by 
the  great  velocity  of  its  rotation.      The  cloudy  zones  are 
more  luminous  than  the  surface  of  the  planet,  on  account  of 
their  more  powerful  reflection  of  the  solar  light. 

(t.  The  belts  are  not  equally  conspicuous,  there  being  two  generally 
which  are  more  distinctly  observable  than  others,  and  more  permanent. 
These  are  situated,  one  on  each  side  of  the  equator,  and  are  sepa- 
rated by  a  clear  space  somewhat  more  luminous  than  the  other  parts 
of  the  disc.  Toward  the  poles  they  are  narrower  and  less  dark  ;  and 
they  imperceptibly  fade  away  a  short  distance  from  the  eastern  and 
western  edges  of  the  disc, — a  phenomenon  due,  evidently,  to  the  thick- 
ness of  the  atmosphere  at  those  parts.  Dark  spots  are  also  occa- 
sionally seen  in  connection  with  the  belts. 

In  Fig.  105  are  given  two  telescopic  views  of  this  planet ;  the  first,  from 
a  drawing  by  Sir  John  Herschel,  as  it  appeared  September  33d,  1833;  the 

QUESTIONS.— ft.  Solar  light  and  heat  of  Jupiter ?  263.  Belts— how  described?  254. 
Their  cause  ?  a.  What  variations  in  appearance  ? 


178  JUPITER. 

second,  by  Madler,  in  1834.    The  two  dark  spots  shown  in  the  latter  were 
employed  to  determine  the  time  of  the  planet's  rotation. 

Fig.  105. 


TELESCOPIC  VIEWS   OF   JtJPITi:tt. 


b.  Notwithstanding  the  cloudy  masses  with  which  the  atmosphere 
appears  to  be  charged,  it  is  not  thought  that  the  latter  has  any  very 
great  height  above  the  planet's  surface ;  for  if  such  were  the  case  the 
edges  of  the  disc,  instead  of  being  sharply  defined  as  we  see  them, 
would  be  nebulous  and  indistinct. 


SATELLITES  OF  JUPITER. 

255.  The  four  satellites  of  Jupiter  are  among  the  most 
interesting  bodies  of  the  solar  system.  They  were  first  seen 
by  Galileo,  in  1610,  a  short  time  after  the  invention  of  the 
telescope,  and  were  perceived  to  be  satellites  by  their  appa- 
rent movements  with  respect  to  the  planet,  alternately 
approaching  it,  passing  behind  it,  and  receding  from  it; 
sometimes  also  passing  over  its  disc  and  casting  their 
shadows  upon  it. 

a.  These  planets  have  been  distinguished  by  particular  names, 

QUFBTIONS.— ft.  Atmosphere  ?     255i  Satellites>~-by  whom  discovered  ?     Their  appa- 
rent motions  ?    a.  How  designated  ? 


JUPITER  179 

but  are  more  generally  designated  by  the  numerals  I.,  II.,  III.,  IV., 
according  to  their  order  from  Jupiter 

256.  Their  PERIODIC  TIMES  are,  respectively,  ld  18h ;  3d 
13h ;  7d  4h;  and  16d  lGh.     The  longest,  it  will  be  seen,  is  but 
a  little  more  than  half  that  of  the  moon. 

«.  It  will  also  be  perceived  that  the  second  is  very  nearly  twice  the 
first ;  and  the  third,  twice  the  second. 

257.  Their  diameters  in  approximate  numbers,  are  L,  2,300 
miles ;  II.,  2,070  miles ;  III.,  3,400  miles ;  IV.,  2,900  miles ; 
all,  excepting  the  second,  being  larger  than  the  moon 

a.  These  figures  are  based  upon  the  measurements  of  their  discs  and 
a  comparison  of  their  apparent  diameters  with  that  of  the  planet  as 
seen  simultaneously.    Thus,  suppose  the  apparent  diameter  of  Jupiter 
in  opposition  is  found  to  be  45",  and  the  third  satellite  is  measured  at 
H"  ;  the  diameter  of  the  satellite  must  then  be  &  that  of  the  primary 
planet,  and  85,000  X  &  =  3,400. 

b.  As  seen  from  Jupiter  these  bodies  present  quite  large  discs  ;  the 
apparent  diameter  of  I.  being  36' ;  of  II.,  19' ;  of  III.,  18' ;  and  of  IV., 
9'.    The  first  is  therefore  somewhat  larger  in  appearance  than  that  of 
the  moon.    The  firmament  of  Jupiter  must  present  a  very  beautiful 
diversity  of  phenomena.     These  various  moons,  all  of  which  are  occa- 
sionally above  the  horizon  at  one  time,  go  through  their  phases  within 
a  few  days ;  the  first  within  42  hours.     To  an  inhabitant  of  the  first 
satellite,  the  apparent  diameter  of  Jupiter  must  be  19° ;  that  is,  about 
86  times  as  great  as  the  moon  ;  while  the  amount  of  illuminated  sur- 
face presented  by  it  must  be  nearly  1300  times  as  great. 

c.  Although  their  volumes  are  quite  large,  their  masses  are  very 
inconsiderable,  owing  to  their  very  small  densities,  which  are  I.,  JG  ', 
II.,  -sfe  ;  III.,  h ;  IV.,  -A,  the  earth  being  1.    All  are,  thus,  considerably 
lighter  than  water,  and  the  first  very  much  lighter  than  cork. 

258.  Their  DISTANCES  from    Jupiter    are,    respectively, 
264,000  miles,  423,000  miles,  678,000  miles,  and  1,188,000 
miles. 

a.  These  are  found  by  measuring  their  greatest  elongations  from 

QUESTIONS. -256.  Periodic  times  of  the  satellites  ?  15T.  Their  diameters  ?  a.  How 
found?  /*.  Apparent  size  at  Jupiter?  Apparent  size  of  Jupiter  at  satellites?  c. 
Masses  and  densities  ?  253.  Their  distances  from  the  primary  ?  a.  How  found  T 


180  JUPITER. 

the  planet,  and  comparing  these  with  its  apparent  diameter.  Thus, 
the  greatest  elongations  are  respectively,  136",  217",  349",  and  611"; 
the  apparent  equatorial  diameter  of  the  planet  being  45".  Dividing  each 
elongation  by  45",  we  find  the  ratio  to  the  planet's  diameter  of  the 
distances  of  the  satellites  respectively.  These  are  nearly  I.,  3  ;  II.,  4.8 ; 
III.,  7.7;  IV.,  13.6.  Fig.  106  shows  the  comparative  extent  of  these 
elongations. 

Fig.   106. 


JUPITKR  AND  ITS   SATELLITES  AT  THEIB  OBEATE8T  ELONGATIONS. 

b.  The  entire  system  of  Jupiter  is  thus  comprehended  within  a  circular 
space  of  less  than  2|-  millions  of  miles  in  diameter,  and  subtends  at  its 
distance  from  the  earth  an  angle  less  than  22',  or  about  f  the  apparent 
diameter  of  the  moon.    A  telescope,  the  field  of  view  of  which  would 
include  one-half  the  area  of  the  moon's  disc,  would  exhibit  Jupiter  and 
all  his  satellites,  as  represented  in  Fig.  106. 

c.  A  comparison  of  the  periodic  times  and  distances  as  above  given 
will  prove  that  they  agree  with  Kepler's  third  law.    Thus,  taking  I. 
and  II.  as  an  example,  we  find  ($!)2  =  41  (nearly),  and  (IH)3=  4.1 
(nearly) ;  hence,  (85)2 :  (42)2 : :  (423,000)3  :(264,000)3. 

259.  The  ORBITS  of  these  bodies  are  almost  circular,  and 
very  nearly  in  the  plane  of  the  planet's  equator.      They 
therefore  make  only  a  very  small  angle  with  the  plane  of  its 
orbit  (about  3°). 

260.  The  ECLIPSES,  OCCULTATIONS,  and  TRANSITS  of  the 
satellites  present  an  endless  series  of  interesting  and  useful 
phenomena ;  and  the  situation  of  their  orbits  causes  them 
to  occur  with  very  great  frequency. 

a.  I.,  II.,  and  III.  are  eclipsed  at  every  revolution :  but  so  peculiarly 
related  to  each  other  are  their  motions  that  their  simultaneous  eclipse 
is  impossible.  Laplace  demonstrated  that  the  mean  longitude  of  I., 
plus  twice  that  of  III ,  minus  three  times  that  of  II.,  is  always  equal  to 

QUESTIONS.— ft.  Angular  space  covered  by  the  system?  c.  Kepler's  law — how 
applied?  259.  Figure  and  position  of  the  orbits?  260.  Eclipses?  Why  frequent?  a. 
Ho'V  many  eclipses  may  occur  at  Jupiter  during  a  Jovian  year  ? 


JUPITER.  181 

180°.  Hence,  when  two  are  eclipsed,  the  other  must  "be  on  the  oppo- 
site side  of  the  planet.  This  is  called  the  libration  of  the  satellites, 
All  four  are,  however,  occasionally  invisible,  being  concealed  either 
behind  or  in  front  of  the  planet.  This  occurred  last  in  August,  1867.  It 
has  been  computed  that,  during  a  year  of  Jupiter,  an  inhabitant  of  the 
planet  might  behold  4,500  solar  and  lunar  eclipses. 

b.  During  the  transits  the  satellites  appear  like  bright  spots  passing 
from  east  to  west  across  the  disc,  preceded  or  folio  wed  by  their  shadows, 
which  seem  like  small  round  dots  as  black  as  ink. 

Vis-  107. 


ECLIPSES,  OOOTTLTATUVNB,    ATTH  TRANSITS    OP  JUTITKli's  SATELLITES. 

In  Fig.  107,  to  an  observer  at  E,  I.  is  represented  as  eclipsed ;  II.,  as  just 
passing  into  the  shadow  of  the  planet ;  III.,  just  before  a  transit,  the  shadow 
vreceding ;  and  IV.,  at  the  point  of  occultation.  At  E',  I.  has  just  passed  behind 
the  disc ;  IL  is  in  occultation  ;  III.,  a  transit,  both  shadow  and  satellite  being 
on  the  disc,  the  shadow  preceding ;  IV.,  just  emerging  from  behind  the 
planet ;  at  E",  I.  and  II.  are  behind  the  disc,  III.  is  in  transit,  but  the 
fhadow  follows  the  satellite;  IV.,  just  after  an  eclipse. 

261.  Since  the  occurrence  of  these  eclipses  can  be  exactly 
predicted,  they  serve  to  mark  points  of  absolute  time ;  so 
tbat  if  the  precise  moment  at  which  they  will  occur  at  any 

QUESTIONS  —  b.  How  do  the  satellites  app.ar  in  a  transit?  261.  Why  are  these 
eclipses  useful  f 


182  SATUKK. 

particular  place  has  been  computed,  and  the  actual  time  of 
their  occurrence  at  any  other  place  is  noted,  a  comparison 
of  the  two  will  give  the  difference  of  time,  and,  of  course, 
the  difference  of  longitude,  between  the  two  places. 

a.  Thus,  if  a  mariner  perceives,  by  the  nautical  almanac,  that  the 
eclipse  of  a  satellite  will  occur  at  9  o'clock  P.M.,  Washington  time, 
and  he  notices  that  the  eclipse  does  not  take  place  till  11  o'clock  P.M., 
he  can  infer  that  his  position  is  2  hours,  or  30°,  east  of  Washington. 

b.  Velocity  of  Light  found  by  the  Eclipses  of  Jupiter's   Sat- 
ellites.— In  the  prediction  of  these  eclipses,  a  constant  variation  was  for 
several  years  found  to  exist  between  the  calculated  and  observed  time 
of  the  occurrence,  with  this  additional  fact,  that  the  eclipse  was  later 
as  Jupiter  receded  from  the  earth  and  earlier  as  it  approached  the 
earth  ;  being  about  16m  35£B  earlier  in  opposition  than  in  conjunction. 
These  observations  were  made  by  Olaus  Roemer,  a  Danish  astronomer ; 
and  in  1675  he  promulgated  the  theory,  to  account  for  the  phenomena, 
that  the  passage  of  light  from  a  luminous  body  is  not  instantaneous, 
but  moves  with  a  certain  definite  but  immense  velocity,  requiring  16m 
35£»  to  cross  the  earth's  orbit     This  theory  has  been   universally 
accepted,  and  certain  experiments  recently  made  in  France,  by  M. 
Fizeau  and  others,  have   confirmed  it.    The  velocity  of  light  must 
therefore  be  184,000  miles  a  second.    For  183,000,000  miles  (distance 
across  the  earth's  orbit)  divided  by  995^  (number  of  seconds  in  16™ 
35^),  gives  184,000  (nearly)     Light  must  therefore  require  8i  min- 
utes to  pass  from  the  sun  to  the  earth.    So  great  a  velocity  is  entirely 
inconceivable. 

III.  SATURN      b 

262.  SATURN,  the  second  of  the  major  planets,  is  the 
centre  of  a  very  large  and  peculiar  system,  being  attended 
by  eight  satellites  and  encompassed  by  several  rings.  It 
shines  with  a  dull  yellowish  light. 

a.  Name  and  Sign.— Saturn,  in  the  ancient  mythology,  was  one  of 
the  older  deities,  and  presided  over  time,  the  seasons,  etc.  He  was 
represented  as  a  very  old  man  carrying  a  scythe  in  one  hand.  The 
sign  of  the  planet  is  a  rude  representation  of  a  scythe. 

QUESTIONS.— a.  Illustration?  ft.  What  important  dte-overy  made  by  Roemer?  In 
vrhatway?  What  is  the  velocity  of  light  ?  262.  General  description  of  Saturn?  a. 
Name  and  sign  ? 


SATURH.  183 

263.  The  aphelion  distance  of  Saturn  is  about  921  mil- 
lions of  miles;  the  perihelion  distance,  823  millions;  the 
mean  distance  being  therefore  872  millions. 

«.  This  is  nearly  twice  the  distance  of  Jupiter,  between  which  and 
Saturn  there  is  a  vast  space  of  nearly  400  millions  of  miles,  in  linear 
breadth,  through  which  there  rolls  no  planetary  body.  Light  requires 
about  Uk  to  pass  from  the  sun  to  Saturn. 

264  The  ECCENTRICITY  of  Saturn's  orbit  is  nearly  50 
millions  of  miles,  or  about  .056  of  its  mean  distance,  being 
but  little  greater,  relatively,  than  that  of  Jupiter, 

265»  The  INCLINATION  OF  ITS  ORBIT  to  the  plane  of  the 
ecliptic  is  about  2J°  (2°  29'  36"). 

266.  Its  SYNODIC  PERIOD  is  378  days  (378.07d),  and  its 
SIDEREAL  PERIOD,  10,759  days  or  about  29^  years. 

a.  For  378.07^365 .25*  =  1.03514;  and  378  07* -*• .03514  =  10759* 
(nearly)  The  year  of  Saturn  contains,  therefore,  about  25,000  of  its 
own  days. 

267.  The  greatest  apparent  diameter  of  Saturn  is  21";  its 
least,  14.]".  Its  real  equatorial  diameter  is  about  74,000  miles. 

a.  For  the  least  distance  from  the  earth  is  823  millions  of  miles — 
93  millions  =  730  millions .  and  the  sine  of  10£"  is  about  .000050G8, 
which  being  multiplied  by  730,000,000  will  give  37,000  (nearly)— the 
semi-diameter. 

268.  The  OBLATENESS  of  Saturn  is  greater  than  that  of 
any  other  planet,  being  a  little  more  than  y^  of  its  equatorial 
diameter,  or  7,800  miles. 

a.  Hence  its  polar  diameter  is  only  66,200  miles  ;  its  mean  diame- 
ter being  70,100  miles. 

269.  The  AXIAL  ROTATION  is  performed  in  about  10 J 
hours  (10h  29m  17s). 

«.  This  was  the  determination  reached  by  Sir  William  Herschel  by 


QUESTIONS. — 263.  Distance  from  the  sun  ?  «.  Interval  between  Jupiter  and  Saturn  * 
264.  Eccentricity?  265.  Inclination  of  orbit?  266.  Synodic  and  sidereal  periods? 
a.  How  computed  ?  267.  Apparent  and  real  diameters  ?  268.  Oblateness  ?  269.  Time 
of  rotation  ?  a.  How  and  by  whom  found  ? 


184  SATUEN. 

means  of  observations  made  on  the  belts  which,  like  those  of  Jupiter, 
cross  the  planet's  disc.  Subsequent  observations  have  indicated  but 
little  variation  from  it. 

b.  The  equatorial  velocity  of  Saturn  is,  therefore,  more  than  22,000 
miles  an  hour  ;  and  as  its  density  is  very  small,  being  only  /,-  of  the 
earth's,  its  oblateness  should  be,  according  to  the  law  stated  in  Art. 

/24\2 
251,  &,  (  iQL  )  X  V-  =  40i  ;  that  is,  40^  times  as  great  as  the  earth's. 

But  ifo  X  40  £  =  -6V»  =  -1355  (nearly),  or  about  -ft.  So  that  its  observed 
oblateness  is  much  less  than  it  ought  to  be  in  accordance  with  this  law. 
The  measurement  of  Saturn's  apparent  diameter  is,  however,  so  diffi- 
cult, in  consequence  of  the  rings,  that  there  may  be  considerable  error 
in  the  statement  of  its  oblateness  given  above. 

c.  Volume,  Mass,  and  Density.—  The  volume  of  Saturn  as  com- 
pared with  that  of  the  earth,  is  (^VfY3)3  —  695^  ,  and  its  muss  lias  been 
found  to  be  90  ;  hence  its  density  is  (as  above  stated),  90  -^  095  .7  =  -/,- 
(nearly  )t  the  earth's  being  1;    or  5^  X  /j  =.726  as  compared  with 
water  ;  that  is,  somewhat  lighter  than  oak  wood. 

d.  Superficial  Gravity.  —  This  must  be,  according  to  the  figures 
above  giifen,  (•&%-)*  X  90  =1.15  (nearly).    Hence,  a  body  at  the  sur- 
face of  Saturn  weighs  only  about  |  more  than  at  the  surface  of  the 
earth,  notwithstanding  the  immense  size  of  that  planet. 


The  INCLINATION-  OF  ITS  AXIS  toward  the  plane  of 
its  orbit  is  about  27°  (26°  48'  40"),  or  a  little  greater  than 
that  of  the  earth. 

a.  That  is,  its  axis  makes  an  angle  of  27°  with  &  perpendicular  to  its 
orbit.     The  angle  which  it  makes  with  the  plane  of  its  orbit  is  90°  — 
27°  =  63°      The  position  of  the  axis  is  such  that  its  inclination  toward 
the  plane  of  the  ecliptic  is  about  28°  10'  ;  and  like  that  of  the  earth 
and  those  of  the  other  planets,  as  far  as  it  has  been  ascertained,  the 
axis  remains  parallel  to  itself  during  the  orbital  motion. 

b.  The  Seasons  of  Saturn  must  therefore  be  similar  to  those  of 
the  earth,  but  like  the  year,  29^  times  as  long. 

c.  Solar  Light  and  Heat—  The  distance  of  Saturn  from  the  sun 

QUESTIONS.—  ft.  How  floes  the  oblateness,  computed  by  -Velocity  and  mass,  compare 
\rith  that  found  by  observation?  c.  Volume,  mass,  and  density  ?  </.  Siiperfici-l  grav- 
ity? 270.  Inclination  of  axis  to  the  plane  of  its  orbit?  a.  To  the  plane  of  the  ecliptic  ? 
6.  Seasons  of  Saturn  ?  Solar  light  and  heat  ? 


SATURN.  185 

being  more  than  9£  times  as  great  as  the  earth's,  the  apparent  diameter 
of  the  sun  must  be  less  in  the  same  proportion,  or  82'  -5-  9^  =  3'  22". 
Hence  the  light  and  heat,  considered  with  reference  to  distance,  must 
be,  compared  with  the  earth's,  as  (202"/  to  (1920")2,  or  as  1  to  (9.53)8 ; 
that  is,  only  -y1,-  of  the  earth's. 

271.  SATURN'S  BELTS. — This  planet,  when  viewed  with  a 
good  telescope,  appears  to  be  encompassed  with  dusky  belts ; 
but  they  are  far  more  indistinct  than  those  of  Jupiter ;  and 
instead  of  crossing  the  disc  in  straight  lines  like  those  of 
that  body,  they  generally  present  a  curved  appearance, — an 
indication  of  the  axial  inclination. 

a.  Sir  William  Herschel  inferred  the  existence  of  a  dense  atmos- 
phere surrounding  Saturn,  both  from  the  changes  constantly  occurring 
in  the  number  and  appearance  of  the  belts,  and  the  appearance  of  the 
satellites  at  the  occurrence  of  occupations.  The  nearest  was  observed 
to  cling  to  the  edge  of  the  disc  about  twenty  minutes  longer  than 
would  have  been  possible  had  there  been  no  atmosphere  to  refract  the 
light.  Indications  of  accumulations  of  ice  and  snow  at  the  poles  have 
also  been  detected,  similar  to  those  of  Mars. 

272.  KINGS. — Saturn   is  encompassed  by  three  or  more 
thin,  flat  rings,  all  situated  exactly  or  very  nearly  in  the 
plane  of  its  equator. 

a.  History  of  their  Discovery. — In  his  first  telescopic  examina- 
tion of  this  planet,  Galileo  noticed  something  peculiar  in  its  form.  As 
seen  through  his  imperfect  instrument,  it  appeared  to  him  to  have  a 
small  planet  on  each  side ;  and  hence,  he  announced  to  Kepler  the 
curious  discovery  that  "  Saturn  was  threefold ;"  but  continuing  his 
observations,  he  saw,  to  his  great  astonishment,  these  companion 
bodies  (as  he  thought)  grow  less  and  less,  and  finally  disappear.  For 
fifty  years  afterward  the  true  cause  of  the  appearance  remained  un 
known,  the  distortion  of  the  planet's  form  being  supposed  to  arise  from 
two  handles  attached  to  it  Hence  they  were  called  an«B,'the  Latin 
word  for  handles.  Huyghens,  in  1659.  discovered  the  real  cause  of  the 
phenomenon,  and  announced  it  in  these  words ;  "  The  planet  is  sur 
rounded  by  a  slender,  flat  ring,  everywhere  distinct  from  its  surface, 


QUESTIONS. — 211,  How  do  the  belts  appear  ?    a.  What  indications  of  an  atmosphere  ? 
2T2.  What  rings  encompass  Saturn  T    a.  History  of  their  discovery  ? 


18G  SATURN. 

and  inclined  to  the  ecliptic."  The  division  of  the  ring  into  two  was 
discovered  by  an  English  astronomer  in  1665.  We  have  now  certain 
knowledge  of  the  existenca  of  three  rings,  and  some  indications  of 
several  more. 

273.  Two  of  these  rings  are  very  distinctly  observed,  and 
are  designated  the  interior  and  the  exterior  ring.  The  former 
is  about  16,500  miles  wide ;  the  latter,  10,000  miles.     The 
distance  of  the  interior  ring  from  the  planet  is  about  18,350 
miles ;  and  the  interval  between  these  rings,  about  1,700 
miles.    The  thickness  of  the  rings  does  not  exceed  250 
miles,  and  may  be  much  less. 

€i.  The  diameter  of  the  exterior  ring,  at  the  mean  distance  of  the 
planet,  subtends  an  angle  of  40'',  and  is,  consequently,  nearly  170,000 
miles.  It  will  thus  be  evident  that  1"  of  angular  space  at  the  distance 
of  Saturn  is  equal  to  nearly  4,250  miles  ;  so  that  if  the  ring  were  250 
miles  in  thickness,  it  would  subtend  only  about  -2V'.  The  difficulty  of 
determining  this  precisely  will  at  once  be  obvious.  The  mass  of  the 
ring  has  been  computed  to  be  equal  to  the  118th  part  of  the  planet's 
mass,  from  its  effect  in  disturbing  some  of  the  satellites ;  and  this  would 
prove,  if  its  density  is  equal  to  that  of  the  planet,  that  its  thickness  is 
about  140  miles. 

274.  Within  the  interior  ring  there  is  a  dusky  or  semi- 
transparent    ring,    having    a  crape-like   appearance   as   it 
stretches  across  the  bright  disc  of  the  planet.   (See  Fig.  108.) 

a.  None  of  the  early  observers  noticed  this.  In  1838,  the  Prussian 
astronomer,  Qalle,  perceived  a  gradual  shading  off  of  the  interior  ring 
toward  the  planet.  His  announcement  of  the  fact  elicited  no  attention 
until,  in  1850,  the  distinguished  astronomer  of  our  own  country, 
G.  P.  Bond,  plainly  discovered  and  announced  (Nov.  11)  the  existence 
of  this  dusky  ring;  before,  however,  the  intelligence  had  reached 
England,  the  discovery  had  been  made  (Nov.  18)  there  also,  by  the 
celebrated  observer,  Dawes.  The  transparency  of  this  ring  was  fully 
established  in  1852  by  Dawes  and  Lassell.  There  are  also  very  decided 
indications  that  this  dark  ring  is  also  double. 


QUESTIONS.— 2T3.  Principal  rings — their  dimensions?    a.  Diameter  of  exterior  ring t 
Thickness  of  rings?    274.  Dusky  ring?    a.  History  of  its  discovery? 


SATURN. 


187 


Fig.  108  shows  the  planet  as  seen  by  Dawes  in  1852.    The  form  and 
partial  transparency  of  the  dark  ring  are  clearly  represented ;  the  interval 

Fig    1O8. 


TKL1.80OPIO  VIEW   OF   BATUKX. —  D(MVeS. 

between  the  interior  and  exterior  rings  is  also  visible,  as  well  as  the  line 
hi  the  latter,  supposed  to  indicate  another  division  of  the  rings. 

b.  Rotation  of  the  Rings. — It  was  discovered  by  Sir  William  Her- 
schel,  by  observing  certain  bright  spots  seen  on  the  surface  of  the  rings, 
that  they  rotated  on  an  axis  perpendicular  to  their  plane,  and  very  nearly 
coincident  with  that  of  the  planet.     The  time  of  rotation  is  about  10* 
82m,  which  is  the  time  required  by  a  satellite  situated  at  a  distance 
from  the  planet  equal  to  the  centre  of  the  rings,  to  perform  its  revolu- 
tion, according  to  Kepler's  third  law.    As  the  planet  revolves  around 
the  sun,  the  rings  constantly  remain  parallel  to  themselves. 

c.  Stability  of  the  Rings. — Observations  of  great  delicacy  have 
shown  that  the  rings  are  not  exactly  concentric  with  the  planet,  the 
centre  of  gravity  of  the  former  revolving  in  a  small  orbit  round  that 
of  the  latter ;  and  Laplace  showed  that  this  is  an  essential  condition 
of  their  stability ;  since,  if  they  were  precisely  concentric,  a  very  slight 
disturbance,  such  as  the  attraction  of  a  satellite,  would  be  sufficient  to 
destroy  their  equilibrium  and  finally  precipitate  them  upon  the  planet. 

d.  Physical  Constitution  of  the  Rings — The  rings  are  evidently 

QUESTIONS. — ft.  Rotation  of  the  rings?    r.  Are  the  rin(?s  concentric  with  the  planet? 
d.  Why  hare  the  rings  been  supposed  to  be  fluid  ?    What  other  hypothesis. 


188  SATUEN. 

opaque,  since  they  cast  a  shadow  upon  the  planet  and  are  in  tuna 
obscured  by  that  of  the  planet  itself ;  and  it  was,  until  quite  recently, 
thought  that  they  consisted  of  solid  matter.  This,  however,  is  now 
generally  considered  to  be  at  variance  both  with  theory  and  observa- 
tion ;  it  being  shown  that  the  equilibrium  of  solid  rin^s  could  not  long 
be  preserved,  except  by  an  arrangement  which  certainly  clocs  not 
exist.  Moreover,  severe!  subordinate  divisions  have  been  rcmaikcd  in 
the  bright  rings,  portions  of  which  are  of  a  different  shade,  presenting  tie 
"  appearance  of  lour  or  five  concentric  and  deepening  bands,"  compared 
oy  Lassell  to  the  "  steps  of  an  ampitheatre."  These  shaded  bands  and 
the  lines  which  separate  them  do  not  always  present  exactly  tLe  same 
appearance.  The  idea  has  therefore  been  entertained  that  the  rings 
iniglit  be  fluid,  not  only  from  the  circumstances  above  enumerated,  but 
because  minute  observations  disclose  the  fact  that  the  rings  have 
become  broader  and  thinner  than  they  were  when  first  discovered.  A 
more  generally  received  hypothesis  is,  that  the  rings  consist  of  vast 
numbers  of  satellites  revolving  around  the  planet ;  and  that  being 
more  sparsely  scattered  in  the  dark  ring,  they  reflect  the  light  im- 
perfectly and  disclose  the  bright  disc  of  the  planet  between  them 
This  hypothesis  not  only  explains  all  the  phenomena  of  the  rings,  but 
is  consistent  with  other  \  Leucmena  presented  by  tLe  solar  system,  to 
be  referred  to  hereafter. 

275.  APPEARANCE  OF  THE  RINGS. — The  rings,  although 
circular,  appear  like  ellipses  because,  being  inclined  to  the 
plane  of  the  ecliptic,  they  are  always  viewed  obliquely. 
They  become  invisible  when  the  daik  side  is  turned  toward 
the  earth ;  and,  when  its  edge  only  is  presented,  arc  seen,  in 
very  powerful  telescopes,  as  a  mere  thread  of  light,  cutting 
the  disc  of  the  planet.  Sometimes  the  satellites  appear  along 
this  thread  like  a  series  of  brilliant  beads  on  a  string. 

ft.  The  edge  only  of  the  rings  is  seen  when  their  plane  if  prolonge 
would  pass  through   the  earth;  also  when  the  same  plane  pass 
through  the  sun,  so  that  the  edge  only  is  illuminated.     In  each 
these  cases,  the  rings  must  disappear  or  present  only  a  thread 
light.     They  disappear  also  when  their  unillumined  side  is  turne 

QUESTIONS.— 275.  Appearance  of  the  rings?    When  do  they  disappear?    a.  Wht 
is  the  edge  only  seen  ?    When  is  the  dark  side  presented  ? 


SATURN.  189 

toward  the  earth,  which  must,  of  course,  occur  when  their  plane  passes 
bstween  the  earth  and  sun,  so  that  the  rays  of  the  latter  fall  only  on 
that  side  of  the  rings  which  is  turned  away  from  the  earth. 

Fi*.  1O1. 


BATUEN  IN  IMFFKBENT  PARTS  OF  ITS  OBBIT. 

Fig.  109  represents  Saturn  in  different  parts  of  its  orbit,  the  direction  of 
the  axis  and  the  position  of  the  plane  of  the  rings  constantly  remaining  the 
same.  At  A  or  E,  the  time  of  the  planet's  equinox,  the  plane  of  the  rings 
passes  through  the  sun,  so  that  its  edge  only  is  illuminated,  wherever  the 
earth  may  be  situated,  which  is  to  be  conceived  as  revolving  in  a  small 
orbit  within  that  of  Saturn.  At  the  solstice  C,  the  southern  side  of  the 
rings  is  exhibited ;  and  at  G,  the  northern  side.  At  the  intermediate  points 
the  rings  are  viewed  obliquely.  It  will  be  obvious  that,  owing  to  the  com- 
paratively small  size  of  the  earth's  orbit,  the  plane  of  the  rings  can  pass 
through  the  earth,  or  between  it  and  the  sun,  only  a  short  time  before  or 
after  the  equinox,  and,  as  this  must  occur  at  each  equinox,  that  the  disap- 
pearance of  the  rings  from  this  cause  must  occur  twice  during  each  sidereal 
revolution  of  the  planet,  or  at  intervals  of  14*  years.  The  last  disappear- 
ance took  place  in  1862 ,  the  next  will  occur  in  1877.  At  the  present  time 
(18G7),  the  northern  surface  of  the  rings  is  visible. 

276.  SATELLITES.— Saturn  is  attended  by  eight  satellites, 
Seven  of  which  revolve  very  nearly  in  the  plane  of  its 

{uator,  the  orbit  of  the  eighth,  or  most  distant  satellite, 

.aking  with  that  plane  an  angle  of  12|°. 

a.  Names.— The  names  of  these  satellites  in  the  order  of  their  dis- 
ances  from  Saturn,  beginning  with  the  nearest,  are  the  following : — 

QUESTIONS. -2f  6.  How  many  satellites  attend  Saturn?  The  situation  of  their  orbits? 
'-.  How  named? 


190 


SATURN. 


1.  Mimas,  2.  Enceladus,  3.  Tethys,  4.  Didne,  5.  Ehea,  6.  Titan,  7.  Hy 
perion,  and  8.  Japetus, 

b.  History  of  their  Discovery. — Titan  was  discovered  by  Huy- 
ghens,  in  1665 ;  Tethys,  Dione,  Rhea,  and  Japetus,  by  Cassini,  within 
about  twenty  years  afterward ;  Mimas  and  Enceladus,  by  Sir  William 
Herschel,  in  1787  and  1789  ;  and  Hyperion  was  discovered  by  Lassell,  at 
Liverpool,  and  by  Bond,  at  Cambridge,  Mass.,  on  the  same  evening > 
September  19, 1848. 

c.  The  following  are  their  periods  and  distances  from  the  primary ; 


PEBOD6. 

DISTANCES. 

PERIODS. 

DISTANCES. 

1.  MIMAS 

tt| 

121,000       I   6.  RHEA 

4    12V, 

343,000 

2v  ENCELADUS 

Id    9h 

155,0;M)       j  j  C.  TITAN 

16   23. 

7C  6,000 

8.  TETHYS 

l«121h 

191,000 

7.  HYPEEION  j      21  »    7h 

1,006,000 

4»  DIONE 

2   IS- 

246,00) 

j  8.  JAPETUS            79  1    8- 

2,313,000 

277.  The  largest  of  the  satellites  is  Titan,  its  diameter 
being  3,300  miles,  which  is  larger  than  that  of  Mercury* 
The  sizes  of  the  others  are  very  much  less. 

a.  That  of  Japetus  is  1,800  miles ;  Rhea,  1,200 ;  Mimas ;  1,000 
Tethys  and  Dione,  500 ;  Enceladus  and  Hyperion,  unknown. 

b.  The  orbit  of  Japetus  subtends  an  angle  of  only  21  ^  ;  so  that  this 
magnificent  system  of  Saturn  with  his  rings  and  eight  satellites,  at 
its  immense  distance  from  the  earth,  is  contained  within  a  space  in  the 
heavens  less  than  one-half  the  disc  of  the  moon. 

c.  In   1862,  while  the  ring  was  invisible,  the  rare  phenomenon 
occurred  of  a  transit  of  Titan  across  the  disc  of  the  primary.     T1 
Shadow  was  observed  by  Dawes  and  others.     The  same  phenome' 
was  observed  by  Sir  William  Herschel  in  1789. 

d.  The  variations  in  the  light  of  Titan  indicated  to  Sir  V 
fierechel  an  axial  rotation  of  the  satellite,  which,  like  that  of 
Satellites  whose  periods  have  been  discovered,  is  performed  in 
time  as  the  revolution  around  the  primary. 

278.  The  CELESTIAL  PHENOMENA  at  Saturn  mr 

QUESTIONS. — 6.  History  of  their  discovery  ?  c.  Their  periods  and  t 
Which  is  the  largest  satellite  ?  Its  size  ?  a.  Diameter  of  each  of  the  i 
6.  Space  in  the  heavens  occupied  by  the  Saturnian  system  ?  c.  Transit  ^  in :  -.*&, 

Celestial  phenomena  at  Saturn  ? 

i  •  i 


URANUS.  18.1 

a  scene  of  extreme  beauty  and  grandeur.  The  starry  vault, 
besides  being  diversified  by  so  many  satellites,  presenting 
every  variety  of  phase,  must  be  spanned,  in  certain  parts  of 
the  planet,  and  during  different  portions  of  its  long  year, 
by  broad,  luminous  arches,  extending  to  different  elevations, 
according  to  the  place  of  the  observer,  and  receiving  upon 
their  central  parts  the  shadow  of  the  planet. 

IV.  URANUS,    tf 

279.  URANUS  was  discovered  in  1781  by  Sir  William 
Herschel.  It  shines  with  a  pale  and  faint  light,  and  to  the 
unassisted  eye  is  scarcely  distinguishable  from  the  smallest 
of  the  visible  stars. 

a.  History  of  its  Discovery. — This  planet  had  been  observed  by 

several  astronomers  previous  to  its  discovery  by  Herschel,  but  had 

been  mapped  ts  a  star  at  least  twenty  times  between  1690  and  1771, 

its  planetary  character  not  having  been  discerned ;  and  even  Ilerschel, 

on  noticing  that  its  appearance  was  different  from  that  of  a  star,  was 

not  aware  that  he  had  discovered  a  new  planet,  but  supposed  it  to  be 

a  comet,  and  so  announced  it  to  the  world,  April  19th,  1781.    It  was, 

however,  in  a  few  months,  evident  that  the  body  was  moving  in  an 

orbit  much  too  circular  for  a  comet ;  but  its  planetary  character,  sug- 

,ated  first  by  Lexell,  in  June,  1781,  was  not  fully  established  until 

i     '3,  when  Laplace  partly  calculated  the  elements  of  its  orbit.     This, 

^er,  does  not  detract  from  the  merit  of  Herschel,  in  making  this 

»y  ;  for,  the  attention  of  astronomers  having  been  called  to  this 

one  of  a  peculiar  character,  and  not  sidereal,  it  was  a  simple 

etermine  whether  it  was  a  planet  or  a  comet.     The  merit  of 

ery  consisted  in  that  delicacy  of  observation,  that  skill  in  the 

-uments,  and,  more  than  all,  that  unfailing  perseverance 

'terized  Herschel,  and  made  him  the  great  astronomer  of 

and    Sign. — Herschel  proposed  to  call  the  new  planet 

QUESTIONS.— 279.  When  and  by  whom  was  Uranus  discovered  ?     Its  appearance  ? 
a.  I  .story  of  its  discovery  ?    b.  Origin  of  the  name  and  sign  > 


1 92  U  R  A  K  U  S . 

"  Georgium  Sidus,"  George's  Star,  in  compliment  to  his  friend  and 
patron,  King  George  III.  This  name  not  being  accepted  by  foreign 
astronomers,  Lalande  proposed  to  name  it  "  Herschel,"  after  its  great 
discoverer  ;  and  by  this  designation  it  was,  for  some  time,  quite  gener- 
ally known.  The  scientific  world  has  now  definitely  settled  upon  the 
name,  suggested  by  Bode,  of  Uranus,  which,  in  the  Grecian  mythology, 
was  the  name  of  the  oldest  of  the  deities,  the  father  of  Saturn,  as 
Saturn  was  the  father  of  Jupiter.  The  name  of  the  discoverer  is, 
however,  partly  connected  with  the  planet  by  the  sign,  which  is  the 
letter  H  with  a  suspended  orb. 

280.  The   aphelion   distance  of  Uranus  is  about   1,836 
millions  of  miles ;    its  perihelion  distance,  1,672  millions ; 
the  mean  distance  being  1,754  millions,  which  is  more  than 
19  times  (19.183)  that  of  the  earth. 

a.  Light  requires  2  hours  33^  minutes  to  pass  from  the  sun  to 
Uranus ;  for  8m  X  19.183  =  153.464"1  =  2h  33^m  (nearly).     Sunrise  and 
sunset  are  therefore  not  perceived  by  the  inhabitants  of  Uranus  for 
two  hours  and  a  half  after  they  really  occur,  for  the  light  which  pro- 
ceeds from  the  sun  when  it  touches  the  plane  of  the  horizon  does  not 
reach  the  eye  until  2^  hours  afterward. 

b.  The  distance  of  this  planet  from  the  sun  is  so  vast  that  the 
greatest  elongation  of  the  earth  as  seen  from  it  is  only  about  2°.  That 
of  Jupiter  is  only  16^°,  while  its  apparent  diameter  is  but  little  greater 
than  that  of  Mercury  as  seen  from  the  earth.     Even  Saturn  departs 
only  about  29°  from  the  sun,  its  apparent  diameter  being  less  than  20". 
The  inhabitants  of  the  planet,  if  any  there  be,  must  therefore  possess 
much  less  opportunity  than  ourselves  to  become  acquainted  with  the 
constituent  members  of  the  great  system  to  which  they  belong. 

281.  The  ECCENTRICITY  of  the  orbit  of  Uranus  is  about 
82  millions  of  miles,  or  about  .047  of  its  mean  distance. 

282.  The  INCLINATION"  OF  ITS  ORBIT  is  less  than  that  of 
any  other  planet,  being  only  46.J'. 

QUESTIONS.— 280.  What  is  its  distance  from  the  sun  ?  a.  What  time  does  light 
require  to  pass  from  the  sun  to  Uranus?  Effect  on  apparent  sunrise  and  sunset?  It. 
Elongations  and  apparent  diameters  of  the  planets  as  seen  from  Uranus?  281.  Eccen- 
tricity of  its  orbit  ?  282.  Inclinatiou  of  its  orbit  ? 


URANUS.  193 

a.  Nevertheless,  so  vast  is  its  distance  that,  at  its  greatest  latitude, 
it  may  depart  from  the  plane  of  the  ecliptic  more  than  24  millions  of 
miles. 

283.  Its  SYNODIC   PERIOD  is  369.65  days ;   and  therefore 
its  sidereal  period  is  30,687  days,  or  about  84  years. 

a.  The  computation  may  be  made  as  in  the  case  of  the  other  planets : 
360.65  -r-  365.25  =  1.012046  +;  that  is,  Uranus  performs  about  .012046  of 
a  sidereal  revolution  during  the  synodic  period.  Hence,  369. 65d  -r-  .012046  = 
30,687d(  nearly)  is  the  sidereal  period. 

6.  In  the  case  of  a  very  distant  planet,  the  sidereal  period  may  be 
readily  found  by  observing  the  daily  arc  of  movement  of  the  planet 
when  in  quadrature  :  for,  at  that  time,  the  line  joining  tne  earth  and 
planet  is  a  tangent  to  the  earth's  orbit  (see  Fig.  28),  so  that,  for  a  short 
time,  the  earth  moves  either  toward  or  from  the  planet,  and  does  not 
affect  the  apparent  motion  of  the  latter ,  while  its  distance  is  so  great 
that  its  geocentric  increase  in  longitude  is  almost  equal  to  its  helio- 
centric. Now,  the  apparent  daily  increase  of  the  longitude  of  Uranus 
in  quadrature  is  42.23",  and  360°  -f-  42.23"  =  30,689,  which  gives  a 
near  approximation  to  the  true  sidereal  period. 

284.  The  greatest  apparent  diameter  of  TJrarius  is  about 
4"  ;  and  as  1",  at  the  least  distance  of  this  planet,  subtends 
8,350  miles,  the  real  diameter  must  be  33,400  miles.     (By 
more  exact  calculations,  it  is  found  to  be  33,247  miles.) 

ft.  The  cblateness  has  not  positively  been  ascertained.  Miidler  esti- 
mates it  to  be  as  much  as  -^  The  volume  of  Uranus  is  about  72£  times 
that  of  the  earth  ;  but  its  mass  is  only  13  times  ;  hence  its  density  is 
less  than  £  that  of  the  earth,  or  about  equal  to  that  of  water. 

285.  As  the  disc  of  Uranus  presents  neither  belts  nor 
spots,  the  period  of  its  rotation  and  its  axial  inclination  still 
remain  unknown.     It  is  thought,  from  the  positions  of  the 
orbits  of  the  satellites,  that  the  inclination  of  its  axis  is 

QUESTIONS.— a.  Possible  distance  from  the  plane  of  the  ecliptic  ?  283.  Synodic  and 
sidereal  periods?  a.  How  calculated  ?  l>.  How  may  the  sidereal  period  be  found  by 
the  daily  increment  of  longitude?  T84.  Apparent  and  real  diameter  of  Uranus  ?  a. 
Oblateness?  Volume?  Mass?  Density?  285.  Diurnal  rotation? 


made  with  the  best  instruments  to  detect  the  others.  In  1847  two  others, 
situated  within  the  orbit  of  the  nearest  discovered  by  Herschel,  were 
detected,  one  by  Lassell  and  the  other  by  O.  Struve. 

&.  The  following  are  the  names  of  these  satellites,  with  their  periods 
and  distances  • 


PERIODS. 

DISTANCES. 

PERIODS. 

DISTANCES. 

1   ABItiL 

2.  UMJHHEI. 

2J  12£h 
41    3p 

123,000       I 
171,000 

3.    TlTANIA 
4.   OliEBOX 

8^11" 

181  17h 

281,000 
376,000 

c.  Their  orbits  are  inclined  to  the  plane  of  that  of  the  primary  at 
an  angle  of  79°  ;  bat,  as  their  motion  is  retrograde,  it  seems  probable 
that  the  poles  have  been  reversed  in  position,  the  south  pole  being 
north  of  the  ecliptic,  and  vice  versa.  The  inclination  is  properly,  there- 
fore, 101°. 

V.    NEPTUNE     ¥ 

287.  NEPTUNE  is  the  most  distant  planet  known  to  belong 
to  the  solar  system.  It  was  first  observed  in  1846  by  Dr.  Galle 
at  Berlin  ;  but  its  existence  had  been  predicted,  and  its  posi- 
tion in  the  heavens  very  nearly  ascertained  by  the  calculations 
of  M.  Leverrier,  in  France,  and  Mr.  Adams,  in  England  ; 
th^se  calculations  being  based  upon  certain  observed  irregu- 
larities in  the  motion  of  Uranus. 


QUESTIONS—  °86.  How  many  satellites  attend  Uranus?  Direction  of  their  orbital 
motion?  ft.  History  of  their  discovery  ?  b.  Names,  periods,  and  distances?  c.  Posi- 
tion of  their  orbits  and  polet  ?  287.  By  whom,  and  how  was  Neptune  discovered? 


NEPTUNE.  195 

a.  History  of  its  Discovery. — The  discovery  of  this  planet  was 
one  of  the  proudest  achievements  of  mathematical  science  in  its  appli- 
cation to  astronomy,  and  afforded  a  more  striking  proof  of  the  truth  of 
the  great  law  of  universal  gravitation  than  had  previously  been  ascer- 
tained. After  the  discovery  of  Uranus,  in  1781,  it  was  ascertained  that 
the  planet  had  several  times  been  observed  by  astronomers,  and  its 
place  recorded  as  a  star.      These  positions  of  the  planet  could  not, 
however,  be  reconciled  with  those  recorded  after  its  actual  discovery ; 
and  observation  soon  showed  that  its  motion  was  at  certain  points 
increased,  and  at  others  diminished,  by  some  force  acting  beyond  it 
and  in  the  plane  of  its  orbit.     These  facts  suggested  the  existence  of 
another  planet,  revolving  in  an  orbit  exterior  to  that  of  Uranus,  and, 
according  to  Bode's  law,  extending  nearly  twice  as  far  from  the  sun. 
Adams  and  Leverrier  almost  simultaneously  undertook   to  find,  by 
mathematical  analysis,  where  this  planet  must  be  in  order  to  produce 
these  perturbations.     The  former  reached  the  solution  of  this  wonder- 
ful   problem  first,  and,  in  October,  1845,  after  three    years  of  toil, 
communicated  to  Mr.  Airy,  Astronomer  Royal,  the  result,  pointing  out 
the  position  of  the  planet  and  the  elements  of  its  orbit.     The  search 
for  the  planet  was  not,  however,  commenced  until  Leverrier  published 
the  result  of  his  labors,  which  was  found  to  agree  so  closely  with  that 
attained  by  Adams,  that  astronomers  both  in  France  and  England 
prepared  to  construct  maps  of  the  part  of  the  heavens  indicated,  in 
order  to  detect  the  planet. 

In  this  they  were  anticipated  by  the  Berlin  observer,  who,  being 
informed  by  Leverrier  of  the  result  of  his  computations,  and  having 
by  a  fortunate  coincidence  just  received  a  newly  prepared  star-map  of 
the  21st  hour  of  right  ascension  (the  part  of  the  heavens  designated  by 
Leverrier),  immediately  compared  it  with  the  stars,  and  found  one  of 
them  missing.  The  observations  of  the  following  evening,  by  detect- 
ing a  retrograde  motion  of  this  star,  established  its  true  character.  It 
was  the  planet  sought  for,  and,  wonderful  to  relate,  was  found  only 
52'  from  the  place  assigned  by  Leverrier.  He  had  also  stated  its  appa-" 
rent  diameter  at  3.3'' ;  it  was  found  by  actual  measurement  to  be  3". 
Adams's  determination  of  the  place  of  the  supposed  planet  differed 
from  the  true  place  by  about  2°. 

b.  Name    and    Sign. — This  planet,   according   t">  the  system  of 
mythological  designations,  was,  after  considerable  discussion,  called 

QUESTIONS. — a.  Circumstances  connected  with  its  discovery?  How  nearly  was  its 
true  place  predicted  ?  ft.  Name  and  sign  ? 


196  NEPTUNE. 

Neptune.    The  sign  is  the  head  of  a  trident — the  peculiar  symbol  of 
this  deity. 

288.  The  APHELION  DISTANCE  of  Neptune  is  2,770  mil- 
lions of  miles ;  its  perihelion  distance,  2,722  millions ;  its 
mean  distance  being  2,746  millions. 

u.  This  is  about  30  times  the  distance  of  the  earth ;  but  according 
to  Bode's  law,  it  should  have  been  38.8  times  ;  so  that  this  remarkable 
relation  of  the  planets,  failing  in  this  instance,  ceases  to  be  a  law,  and 
becomes,  apparently,  only  a  curious  Coincidence. 

b.  So  immense  is  the  distance  of  Neptune  that  only  Saturn  and 
Uranus  can  be  seen  from  it.     If  there  are  astronomers,  however,  on  the 
planet,  they  must  have  much  better  opportunities  than  ourselves  for 
becoming  acquainted  with  the  distances  of  the  stars ;  since,  at  oppo- 
site periods  of  their  long  year,  they  are  situated  at  positions  in  space 
about  5.500  millions  of  miles  apart. 

c.  Since  the  distance  of  Neptune  from  the  sun  is  30  times  that  of 
the  earth,  light  requires  8m  X  30  =  4h,  to  reach  that  planet 

289.  The  ECCENTRICITY  of  the  orbit  of  Neptune  is  about 
24  millions  of  miles,  which  is  only  .0087  of  its  mean"  dis- 
tance ;  so  that  it  is,  relatively,  but  little  more  than  one-half 
that  of  the  earth's  orbit. 

290.  The  INCLINATION  OF  ITS  OKBIT  to  the  plane  of  the 
ecliptic  is  very  small,  being  only  1|°  (1°  47'). 

a.  The  sine  of  1°  47'  is  .031 ;  hence  Neptune,  when  at  its  mean  dis- 
tance from  the  sun,  and  at  the  point  of  greatest  latitude  north  or  south 
of  the  ecliptic,  must  be  more  than  85  millions  of  miles  from  the  plane 
of  that  circle  ;  for,  2.746,000,000  X  .031  =  85,126,000. 

291.  Its  SYNODIC  PERIOD  is  about  3674  days  (367.48234) ; 
hence  its  SIDEREAL  PERIOD  is  60,127  days,  or  about  164.] 
years. 

a.  It  is  more  difficult  to  calculate  the  sidereal  periods  of  these 


QUESTIONS.— 288.  Aphelion,  perihelion,  and  mean  distances  ?  a.  Does  it  agree  with 
Bode's  law  ?  6.  Which  planets  can  he  seen  at  Neptune  ?  c.  How  long  does  light 
require  to  pass  from  the  sun  to  Neptune?  289.  Eccentricity  of  its  orbit?  290.  Incli- 
nation ?  a.  How  far  may  it  depart  from  the  plane  of  the  ecliptic?  How  is  this  calcu- 
lated ?  291.  Synodic  period  ?  Sidereal  period  ?  a.  How  calculated  ? 


NEPTUNE.  197 

remote  planets ;  since  the  synodic  period  is  so  nearly  equal  to  the  side- 
real period  of  the  earth,  that  the  fraction  of  a  revolution  performed 
during  the  latter  is  very  small.  In  the  case  of  Neptune  it  is  a  little 
over  .0061118;  that  is,  367.48234d  -~-  365. 25d=  1.0061118  -f-;  and  367.- 
48234d-=-  .0061118  =  60,127  days  (nearly). 

292.  The  APPARENT  DIAMETER  of  Neptune  when  greatest 
is  2.9"  ;  hence  its  real  diameter  must  be  nearly  37,000  mik-s, 

a.  For  the  least  distance  of  Neptune  from  the  earth  is  2,722  millions 
—  93  millions  =  2,629  millions ;  now  the  sine  of  2.9"  is  .000014  :  and 
2,629  millions  multiplied  by  this  small  fraction  will  give  36,806  miles. 

b.  Volume,  Mass,  and  Density.— The  volume  of  Neptune,  if  cal- 
culated by  the  method  previously  explained,  will  be  found  to  be  very 
nearly  99  times  as  great  as  that  of  the  earth,  and  consequently  is  only 
about  iLf  as  large  as  Jupiter.    Its  mass  is  nearly  17  times  (16.76)  as 
great  as  the  earth's  [Prof,  Pierce]  ;  consequently  its  density  must  be 
about  ^  that  of  the  earth,  or  somewhat  more  than  -^  as  heavy  as  water. 

c.  Solar  Light  and  Heat.  —The  apparent  diameter  of  the  sun  as 
Been  at  Neptune  must  be  a  little  more  thanl'  •,  for,  32  -r-  30.037  (ratio  of 
of  Neptune's  distance  to  the  earth's)— 64"(nearly).  Hence,  the  sun  at  this 
planet  looks  but  little  larger  than  Venus  ;  but  its  light  is  vastly  more 
brilliant.     For,  since  the  intensity  of  light  varies  inversely  as  tne 
square  of  the  distance,  and  (30.037)2  =  902  (nearly),  the  light  at  Nep- 
tune must  be  q{)2  of  that  at  the  earth,  and  hence  is  nearly  equal  to 
that  of  670  full  moons  (157,  6).     This  is  probably  as  great  as  that 
which  would  be  produced  by  20,000  stars  shining  at  once  in  the  firma- 
ment, each  equal  to  Venus  when  its  splendor  is  greatest. 

293.  A  SATELLITE  of  this  planet  was  discovered  by  Lassell 
in  October,  1846,  and  was  afterward  observed  by  several 
other  astronomers. 

a.  From  observations  made  about  the  same  time  the  existence  of 
another  satellite  was  suspected,  as  well  as  a  ring  analogous  to  that  of 
Saturn  ;  but  the  most  diligent  and  careful  scrutiny  with  very  powerful 
telescopes  has  failed  to  detect  any  indications  of  the  truth  of  these 
conjectures. 

QUESTIONS.— 292.  Apparent  diameter  of  Neptune?  Its  real  diameter?  a.  How 
found?  b.  Its  volume,  mass,  and  density?  c.  How  great  is  the  intensity  of  solar 
light  and  heat?  How  found?  293.  By  whom  and  when  was  the  satellite  discovered? 
a.  What  conjectures  as  to  another  satellite,  etc.  ? 


198  NEPTUNE. 

b.  Distance  of  the  Satellite. — The  observations  made  by  eminent 
astronomers  (principally  those  of  M.  Struve,  Mr.  Lassell,  and  Mr. 
Bond)  have  shown  that  the  greatest  elongation  of  the  satellite  from 
its  primary  is  18 ",  the  apparent  diameter  of  the  latter  being  at  the 
same  time  2.8".  Hence  its  distance  must  be  18"  -:-  2.8"  =  6|  diame- 
ters, or  12f-  radii,  of  the  planet :  and  18,500  X  12$  —238,000  miles,  or 
about  the  same  as  the  moon's  distance  from  the  earth. 

C.  Inclination,  Period,  and  Rotation. — The  orbit  of  this  satellite  is 
nearly  circular,  and  is  inclined  to  the  orbit  of  Neptune  in  an  angle  of 
29°.  Its  motion,  like  that  of  the  satellites  of  Uranus,  is  retrograde,  or 
from  east  to  west  Its  sidereal  period,  as  determined  by  Lassell  at  Malta, 
in  1852,  is  5d  21h.  Periodical  changes  in  its  brightness  were  observed 
by  Lassell,  which  indicated  that  this  satellite,  like  others  in  the  sys- 
tem, rotates  on  its  axis  in  the  same  time  that  it  revolves  around  its 
primary. 

d.  Are  there  Planets  beyond  Neptune? — This  is  a  question 
which  we  are  at  present  entirely  unable  to  answer.  Future  genera- 
tions may,  with  greater  resources  of  science  and  mechanical  skill, 
disclose  new  marvels  in  our  system,  and  detect  other  bodies  obedient 
to  the  dominion  of  its  great  central  sun.  The  nearest  of  the  stars  is 
known  to  be  nearly  7,000  times  as  far  from  Neptune  as  that  body  is 
from  the  sun ;  and  it  is  by  no  means  improbable,  therefore,  that  so 
vast  a  space  should  contain  planetary  bodies  reached  by  the  solar 
attraction,  but  very  far  beyond  the  sphere  of  any  other  central  lumi- 
nary. It  will  require,  however,  far  greater  means  than  we  possess  to 
bring  this  to  a  practical  determination. 

QUESTIONS.—  b.  What  is  the  distance  of  this  satellite  from  the  primary?  How  cal 
culated  ?  c.  Its  inclination  of  orbit?  Orbital  revolution— period  and  direction  ?  Axial 
rotation  ?  d,  is  Neptune  the  remotest  planet  ? 


CHAPTER    XIV. 


THE   MINOR   PLANETS,   OE  ASTEROIDS. 

294.  The  MINOR  PLANETS  are  a  large  number  of  small 
bodies  revolving  around  the  sun  between  the  orbits  of  Mars 
and  Jupiter.  The  number  discovered  up  to  the  present 
time  (1869)  is  106. 

a.  Discovery  of  Ceres  and  Pallas. — The  existence  of  so  large  an 
interval  between  Mars  and  Jupiter,  compared  with  the  relative  dis- 
tances of  the  other  planets,  for  a  long  time  engaged  the  attention  and 
incited  the  researches  of  astronomers.  Kepler  conjectured  that  a 
planet  existed  in  this  part  of  the  system,  too  small  to  be  detected  ;  and 
this  opinion  received  considerable  support  from  the „  publication  of 
Bode's  law  in  1772.  When  Uranus  was  discovered,  in  1781,  and  its 
distance  was  found  to  conform  to  this  law,  the  German  astronomers 
became  so  confident  of  the  truth  of  this  bold  conjecture  of  Kepler,  that, 
in  1800,  they  formed,  under  the  leadership  of  Baron  de  Zach,  an  asso- 
ciation of  24  observers  to  divide  the  zodiac  into  sections  and  make  a 
thorough  search  for  the  supposed  planet.  This  systematic  exploration 
had,  however,  been  scarcely  commenced,  when,  in  1801,  Piazzi,  an 
Italian  astronomer,  while  engaged  in  constructing  a  catalogue  of  stars, 
detected  a  new  planet.  It  was  called  by  him  Geres.  In  the  next  year, 
while  looking  for  the  new  planet,  Olbers  discovered  another,  which  he 
called  Pallas. 

b»  Discovery  of  Juno  and  Vesta — Theory  of  Olbers. — The  ex- 
treme minuteness  of  the  new  planets,  and  the  near  approach  of  their 
orbits  at  the  nodes,  led  Olbers  to  suppose  that  they  might  be  the  frag- 
ments of  a  much  larger  planet  once  revolving  in  this  part  of  the 
system,  and  shattered  by  some  extraordinary  convulsion.  Believing 

QUESTIONS. — 294  What  are  the  minor  planets?  Their  number?  a.  How  and  by 
whom  were  Ceres  and  Pallas  discovered  ?  6.  Juno  and  Vesta  ?  Theory  of  Olbers  ? 


200  MINOR    PLANETS. 

that  other  fragments  existed,  and  that  they  must  pass  near  the  nodes 
of  those  already  found,  he  resolved  to  search  carefully  in  the  direction 
of  those  points ;  but  while  he  was  thus  engaged,  Harding,  of  the 
observatory  of  Lilienthal,  discovered,  in  1804,  very  near  one  of  those 
points,  a  third  planet,  which  he  called  Juno.  Olbers,  still  further  stim- 
ulated by  this  event  to  continue  the  investigation  which  he  had 
commenced,  was  at  length,  in  1807,  rewarded  by  discovering  a  fourth 
planet,  Vesta,  near  the  opposite  node.  From  this  date  until  1845,  no 
additional  discovery  was  made.  These  small  planets  were  called 
Asteroids  by  Herschel,  from  their  resemblance,  in  appearance,  to  stars. 

c.  Discovery  of  the  other  Minor  Planets. — In  1845,  M.  Hencke, 
an  amateur  astronomer  of  Driessen,  after  a  series  of  observations  con- 
tinued for  fifteen  years  with  the  use  of  the  Berlin  star-maps,  discovered 
Astrcea,  the  fifth  of  this  singular  zone  of  telescopic  planets.      The 
others  have  been  discovered  in  the  following  order :  In  1847,  Hebe, 
Iris,  Flora  ;  1848,  Metis ;  1849,  Hygeia  ;  1850,  Partheriope,  Victoria, 
and  Egeria  ;    1851,  Ire'ne  and  Eunomia ;    1852,  Psyche,  Thetis,  Mel- 
pom' ene,  Fortu'na,  Massilia,   Lutetia,   Calliope,  and  Thalia;  1853, 
Themis,  Phoce'a  Proserpina,  and  Enter' pe  ;  1854,  Bello'na,  Amphi- 
tri'te,  Urania,  Euphros'yne,  Pomo'na,  and  Polyhym'nia  ;  1855,  Circe, 
Leuco'thea,   Atalan'ta,  and  Fides ;  1856,   Le'da,  Lcetita,  Harmonia, 
Daphne,   and  Isis ;  1857,  Ariadne,  Ny'sa,  Eugenia,  Hestia,  Mel'ete, 
Aglaia,  Doris,  PU'les,  and  Virginia;  1858,  Neman' sa,  Euro'pa,  Ca- 
lypso, Alexandra,  and  Pandora ;  1859,  Mnemosyne ;  1860, Concordia, 
Dan'ae,  Olympia,  Erato,  and  Echo ;  1861,  Ausonia,  Angelina,  Cyb'ele, 
Ma'ia,  Asia,  Hesperia,  Leto,  Panope'a,  Feronia,  and  Ni'obe;  1862, 
Clyt'ie,  Oalate'a,  Euryd'ice,  Fre'ia,  and   Frig'ga;    1863,  Diana  and 
Euryn'ome  ;  1864,  Sappho,  Terpsichore,  and  Alcmene ;  1865, Beatrix, 
Clio,  and  lo  ;  1866,  Sem'ele,  Sylvia,  This"be,  <§>,  Antiope,  ©  ;  1867,  <§> 
<§>,  <8>,  <§>;  1868,®,  ©,  ©,  ®,®,  @>,  <®,  ®»  @>>  @>  (§>•      The 
largest  number  discovered  in  any  single  year  is  eleven  (in  1869);  and  in 
the  three  years,  '57,  '61,  and  '69,  no  less  than  thirty  were  discovered. 

d.  Names  of  the  Discoverers. — Dr.  Luther,  at  the  observatory  of 
Bilk,  near  Dusseldorf,  has  discovered  no  less  than  16,  and  is  at  the 
head  of  planet  discoverers ;   Mr.  Herman  Goldyhmidt,  an  amateur 

QUESTIONS. — c.  What  time  elapsed  before  Ash-sen  was  discovered  ?  Mention  those 
discovered  in  each  subsequent  year.  In  what  year  were  the  largest  number  discov- 
ered? Who  has  discovered  the  greatest  number?  d.  What  other  discoverers  are 
named ?  How  many  of  the  minor  planets  were  discovered  in  the  United  States?  How 
ore  thene  bodies  designated  ? 


MINOR    PLANETS.  201 

astronomer  of  Paris,  has  discovered  14;  Mr.  Hind,  a  distinguished 
English  astronomer,  10  ;  De  Gasparia,  at  Naples,  9  ;  M.  Chacornac,  at 
Marseilles  and  Paris,  6  ;  Mr.  Pogson,  an  English  astronomer,  6  (3  at 
Oxford,  and  3  at  Madras) ;  Dr.  C.  H.  F.  Peters,  at  Clinton,  N.  Y.,  8 ; 
M.  Tempel,  at  Marseilles,  6 ;  Mr.  Ferguson,  at  Washington,  3 ;  Mr.  Wat- 
son, at  Ann  Arbor,  Michigan,  9 ;  Mr.  Tuttle,  at  Cambridge,  Mass.,  2  ; 
several  other  observers,  1  or  2  each.  Twenty-three  of  these  planets  have 
been  discovered  in  this  country.  Instead  of  the  names  above  given,  the 
minor  planets  are  now  generally  distinguished  by  numerals  according  to 
the  order  of  their  discovery.  Several  of  these  bodies  were  discovered  by 
two  or  more  observers  independently. 

295.  The  AVERAGE  DISTANCE  of  these  planets  from  the 
sun  is  about  260  millions  of  miles.     That  of  the  nearest, 
Flora,  is  about  201  millions ;   that  of  the  most  distant, 
Sylvia,  is  nearly  320  millions.     The  entire  width  of  the  zone 
in  which  they  revolve  is,  however,  about  190  millions  of  miles. 

296.  The  INCLINATION  OF  THEIR  ORBITS  is  very  diverse ; 
more  than  one-third  of  the  whole  have  a  greater  inclination 
than  8°,  and  consequently  extend  beyond  the  zodiac.    The 
greatest  is  that  of  Pallas,  amounting  to  34°  42' ;  the  least, 
that  of  Massilia,  which  is  only  41'. 

297.  The  ECCENTRICITY  of  their  orbits  is  equally  variable ; 
the  most  eccentric   being  that  of  Polyhymnia,  which    is 
.337,  or  more  than  one-third ;  the  least  eccentric  is  that  of 
Europa,  which  is  only  .004,  or  ^i^. 

«.  These  orbits  are  not  concentric  ;  but  if  represented  on  a  plane 
surface,  would  appear  to  cross  each  other,  so  as  to  give  the  idea  of 
constant  and  inevitable  collisions.  "  If,"  says  D' Arrest,  of  Copenhagen, 
"  these  orbits  were  figured  under  the  form  of  material  rings,  these  rings 
would  be  found  so  entangled,  that  it  would  be  possible,  by  means  of 
one  among  them  taken  at  a  hazard,  to  lift  up  all  the  rest."  The  orbits 
do  not,  however,  actually  intersect  each  other,  because  they  are  situ- 
ated in  different  planes ;  but  some  of  them  approach  within  very  short 

QUESTIONS.— 205.  Average  distance?  Which  is  the  nearest?  The  farthest?  296. 
Inclination  of  their  orbits?  How  many  heyond  the  zodiac ?  The  most  inclined ?  The 
least?  29T.  Eccentricity?  Greatest?  Least?  a.  Position  of  their  orbits  ? 


202  MINOR    PLANETS. 

distances  of  each  other.  The  orbit  of  Fortuna,  for  example,  approaches 
the  orbit  of  Metis  within  less  than  the  moon's  distance  from  the  earth. 
This  is  also  true  of  the  orbits  of  Astrsea  and  Massilia,  and  those  of 
Lutetia  and  Juno. 

298.  The  LARGEST  of  the  minor  planets  is  Pallas,  the 
diameter  of  which  is  variously  estimated  at  from  300  to  700 
miles.     These  bodies  are  generally  so  small  that  it  is  quite 
impossible  to  measure  their  apparent  diameters,  or  to  say 
which  is  the  smallest.     The  brightest  of  these  planets  is 
Vesta ;    the   faintest,   Atalanta.    Vesta,   Ceres,  and   Pallas 
have  been  seen  with  the  naked  eye,  having  the  appearance 
of  very  small  stars. 

299.  The  SIDEREAL  PERIOD  of  Flora  is  3]    years ;    that 
of  Sylvia  is  about  6^  years.    The   average  period  of  the 
whole  is  about  4}  years. 

a.  Origin   of   the    Minor    Planets. — The   theory   of   Gibers  has 
already  been  alluded  to ;  it  supposes  that  these  little  planets  are  the 
fragments  of  a  much  larger  one,  which  by  an  extraordinary  catastro- 
phe was,  in  remote  antiquity,  shivered  to  pieces.      Prof.  Alexander 
has  endeavored  to  compute  the  size  and  form  of  this  planet     He  sup- 
poses that  it  was  not  of  the  form  of  a  globe,  but  shaped  like  a  lens 
or  wafer,  the  equatorial  and  polar  diameters  being  respectively,  70,000 
miles  and  8  miles  ;  that  the  time  of  its  rotation  was  about  3^  days ; 
and  that  it  burst  in  consequence  of  its  great  velocity,  as  grindstones 
and  fly-wheels  sometimes  do.    This  theory  of  an  exploded  planet  has 
not  been  generally  accepted,  since  it  is  highly  improbable,  and  sup- 
ported by  no  analogous  facts. 

b.  Nebular  Hypothesis. — This  was  invented  by  Laplace  to  account 
for  the  formation  of  the  solar  system  by  the  operation  of  ordinary 
physical  laws.     He  conceived  that  the  matter  of  which  the  various 
bodies  belonging  to  this  system  are  composed,  originally  had  an  enor- 
mously high  temperature  and  existed  in  the  condition  of  gas  or  vapor, 
filling  a  vast  space  ;  that  as  this  mass  cooled,  and,  of  course,  unequally, 
currents  were  formed  within  it,  which,  tending  to  different  points  or 


QUESTIONS.— 298.  Which  is  the  largest  of  the  planets  ?  The  brightest  ?  The  faintest  ? 
299.  Average  sidereal  period  ?  Longest?  Shortest?  a.  Origin  of  the  minor  planets ? 
Asteroid  planet  ?  b.  Nebular  hypothesis  ? 


MINOfi    PLANETS.  203 

centres,  gave  it  finally  a  slow  rotation  ;  that  this  increased  by  degrees, 
until  the  centrifugal  force  exceeded  the  attraction  of  the  central  mass, 
and  a  zone  or  ring  became  detached,  of  a  lower  temperature,  but  still 
vaporous  or  liquid;  and  that  thus  successive  rings  were  formed, which 
breaking  up  as  they  rotated,  the  parts  finally  came  together  and 
formed  spheroidal  masses  revolving  around  the  original  mass.  If  these 
rings  condensed  without  breaking  up  they  would  continue  to  revolve 
as  rings,  like  those  of  Saturn  ;  if,  on  the  other  hand,  they  broke  up 
into  small  parts,  none  sufficiently  large  to  attract  all  the  others,  they 
would  condense  into  fragments  and  continue  to  revolve  as  small 
planets,  like  the  asteroids.  The  larger  planet  masses,  being  still  in  a 
vaporous  condition,  would,  as  they  cooled  and  condensed,  throw  off 
rings  like  the  original  mass  ,  and  in  this  manner  either  satellites  or  rings 
would  be  formed.  The  residue  of  the  original  nebulous  mass  he  con- 
ceived to  be  the  sun. 

Such  is  a  brief  outline  of  this  celebrated  and  most  ingenious 
hypothesis, — an  hypothesis  which  every  subsequent  discovery  has 
seemed  to  harmonize  with  and  confirm.  Whatever  theory  be  adopted 
to  account  for  the  development  of  the  solar  system  and  the  exist- 
ence of  this  zone  of  small  planets,  it  must  not  be  forgotten  that  the 
infinite  power  and  intelligence  of  the  Great  Creator  could  alone 
have  brought  them  into  being.  The  only  question  is,  in  what  way  did 
He  exert  this  power,  and  in  what  manner  did  He  ordain  that  all  these 
wonderful  orbs  should  come  into  existence  as  witnesses  of  His  omnipo- 
tence and  benevolent  design. 

c.  Decrease  in  Brightness  of  the  Successive  Groups. — The 
brightest  of  the  minor  planets  seem  to  have  been  discovered,  for  each 
successive  group  is  less  conspicuous  than  those  preceding  it.  The 
first  ten  resemble  stars  of  the  eighth  magnitude  [the  brightest  stars 
are  of  the  first]  ;  the  last  ten  are  but  little  brighter  than  stars  of  the 
twelfth  magnitude.  It  is  not  anticipated,  therefore,  that  others  will 
hereafter  be  detected  with  the  readiness  and  frequency  which  have 
marked  the  discoveries  of  the  last  ten  years.  The  labor  required  in 
the  discovery  of  these  little  bodies  is  almost  inconceivable.  The 
most  successful  discoverers  have  attained  the  object  of  their  efforts 
only  after  mapping  down  every  minute  star  in  certain  zones  of  the 
heavens ;  and  to  do  this  required  a  patient  and  toilsome  watching 
during  every  clSar  night  for  many  months. 

QUESTIONS.— c.  What  decrease  iti  brightness  is  referred  to  ?  bifificulties  in  discover- 
ing these  bodies  ? 


CHAPTER    XV. 

MUTUAL   ATTRACTIONS   OF  THE   PLANETS. 

300.  The   PLANETS,   while    revolving    around    the   sun, 
constantly  disturb  each  other's  motions,  and  thus  give  rise 
to   numerous   irregularities,  similar   to   those   which   take 
place  in  the  revolution  of  the  moon  around  the  earth. 

301.  These   irregularities  are  called  inequalities   or  per- 
turbations.    They  are  either  periodic  or  secular,  the  former 
requiring  short,  the  latter  very  long  periods  of  time  for  their 
completion. 

€t.  Problem  of  the  Three  Bodies. — To  compute  the  exact  place 
of  a  planet  at  any  time  requires  that  all  the  inequalities  due  to  the 
disturbing  action  of  other  planets  should  be  taken  into  account ;  and 
to  do  this  has  tasked  to  the  utmost  the  highest  powers  of  the  human 
intellect.  The  problem  is,  however,  simplified  by  the  fact  that,  as  the 
sun's  attraction  is  so  much  greater  than  that  of  the  other  bodies,  the 
place  of  the  planet  can  be  found  by  first  supposing  that  it  revolves  in 
an  exact  elliptical  orbit,  and  then  calculating  the  amount  of  disturbance 
due  to  each  other  planet  in  succession  ;  the  aggregate  of  the  results 
thus  obtained  giving  the  proper  correction  to  be  applied  in  order  to 
ascertain  the  true  place.  This  has  been  called  the  The  Problem  of  the 
Three  Bodies,  because  it  involves  the  investigation  of  the  motion  of 
one  body  revolving  around  another,  and  continually  disturbed  by  the 
attraction  of  a  third.  To  determine,  therefore,  all  the  inequalities  to 
•which  any  planet  is  subject,  it  is  necessary  to  solve  this  problem  sepa- 
rately for  every  other  planet  by  which  it  may  be  disturbed.  Its 
complete  solution  surpasses  the  powers  of  the  most  skillful  mathe- 
matician. 


QUESTIONS. — 300.  How  do  the  planets  disturb  each  other?     £01.  What  are  the  irregu- 
larities called  ?    Of  how  many  kinds  ?   «.  What  is  the  "  Problem  of  the  Three  Dodice  ?" 


ATTRACTIONS    OF    THE    PLANETS.  205 

302.  The  ELEMENTS  OF  A  PLANET'S  ORBIT  are  the  facts 
which  it  is  necessary  to  know  in  order  to  determine  the  pre- 
cise situation  of  the  planet  at  any  instant.     They  are — 1. 
Tfie  position  of  the  line  of  nodes  ;  2.  The  inclination  of  the 
orbit  to  the  plane  of  the  ecliptic  ;    3.  The  place  of  the  peri- 
helion ;  4.  TJie  eccentricity ;   5.  Tlie  major  axis. 

a.  Elements  1,  2,  and  8  determine  the  position  of  the  orbit ;  4,  its 
figure  ;  and  5,  its  size.     In  order  to  find  the  place  of  the  planet,  it  is 
necessary  also  to  know  the  periodic  time,  and  the  place  of  the  planet  at 
any  particular  epoch. 

b.  Heliocentric  and  Geocentric  Place. — The  true  position  of  a 
planet  is  that  in  which  it  would  appear  to  be  situated  if  viewed  from 
the  sun,    that  is,  its  heliocentric  place  ;  hence,  one  important  point  in 
ascertaining  a  planet's  true  position  is  to  deduce  its  heliocentric  place 
from  its  geocentric  place,  or  situation  as  seen  from  the  earth. 

303.  The  only  INVARIABLE  ELEMENT  is  the  length  of  the 
major  axis  ;  every  other,  in  the  case  of  each  planet,  under- 
goes certain  small  changes,  such  as  those  which  have  been 
described  in  the  orbits  and  motions  of  the  earth  and  moon. 

«.  Thus  the  inclinations  of  the  orbits  of  Mercury,  Venus,  and 
Uranus  are  increasing  ;  those  of  Mars,  Jupiter,  and  Saturn  are  dimin- 
ishing ;  the  greatest  variation  being  that  of  Jupiter,  which  is  23"  in  a 
century.  A  similar  variation  occurs  in  the  positions  of  the  nodes  and 
perihelion,  and  in  the  amount  of  eccentricity.  In  the  case  of  the  earth, 
as  has  been  stated  (Art.  125,  e),  the  latter  is  diminishing  ;  and  this  is 
also  true  of  Venus,  Saturn,  and  Uranus ;  while  that  of  Mercury,  Mars, 
and  Jupiter  is  increasing.  The  greatest  variation  is  that  of  Saturn, 
which  is  about  .00031  of  its  mean  distance  in  a  century.  This  is  rela- 
tively about  7i  times  as  great  as  that  of  the  earth,  and  amounts 
absolutely  to  about  2,700  miles  a  year ;  while  the  absolute  annual 
variation  of  the  earth's  eccentricity  is  only  36^  miles.  All  these 
changes  are  confined  within  certain  very  narrow  limits,  after  reaching 
which  they  occur  in  an  opposite  direction. 

QUESTIONS.— 302.  What  are  the  elements  of  a  planet's  orbit  ?  a.  What  is  determined 
by  them  ?  What  else  must  be  known  to  determine  a  planet's  place  ?  ft.  What  is  meant 
by  the  heliocentric  and  geocentric  places  of  a  planet  ?  203.  Which  clement  is  In  variable5? 
a.  What  examples  are  given  of  variable  elements  ? 


206  ATTRACTIONS    OF    THE    PLANETS. 

304.  The  MOTIONS  OF  THE  PLANETS  are  retarded  or 
accelerated  by  their  mutual  attractions,  according  to  their 
positions  with  respect  to  each  other  and  to  the  sun  ;  but  as 
action  and  reaction  are  equal  and  in  opposite  directions, 
whenever  one  is  accelerated  the  other  which  acts  upon  it 
must  be  retarded. 

Thus,  in  Fig.  93,  page  151,  the  planet  at  M  must  have  its  motion  accel- 
erated by  that  of  the  earth  at  E,  while  the  latter  must  be  retarded ;  but  the 
acceleration  of  M  is  greater  than  the  retardation  of  E,  because  the  disturb- 
ing force  at  M  acts  more  nearly  in  the  direction  of  the  planet's  motion. 
After  conjunction  this  is  reversed ;  the  motion  of  the  earth  being  accelerated 
and  that  of  the  planet  retarded. 

a.  If  the  planets'  orbits  were  exactly  circular,  the  amount  of  accel- 
eration in  one  part  of  the  orbit  would  be  counterbalanced  by  the 
retardation  in  the  other,  and  the  inequalities  would,   in  a  synodic 
period,  cancel  each  other :  but  as  the  orbits  are  elliptical,  the  successive 
conjunctions  must  occur  at  diffe rent  parts  of  the  orbits,  where  the  plan- 
ets are  at  different  distances  from  each  other ;  so  that  the  inequalities 
must  increase  while  the  conjunctions  occur  in  one  part  of  the  orbit, 
and  diminish  while  they  take  place  in  the  other.     If  the  conjunctions 
always  occurred  in  the  same  part  of  the  orbit,  the  inequalities  would 
constantly  accumulate,  and  the  system  would  be  destroyed.    This  is 
nearly  the  case  with  Jupiter  and  Saturn. 

b.  Great  Inequality  of  Jupiter  and  Saturn. — The  periodic  times 
of  Jupiter  and  Saturn  are  respectively  4,332  days  and  10,759  days ;  and 
hence,  5  of  the  former  are  nearly  equal  to  2  of  the  latter  ;  so  that,  in  5 
revolutions  of  Jupiter,  or  about  59  of  our  years,  the  conjunctions  take 
place  at  nearly  the  same  points  of  their  orbits.     The  synodic  period  of 
these  two  planets  is  19.86  years  :  and  during  the  17th  and  18th  cen- 
turies the  conjunctions  constantly  occurred  almost  at  their  points 
of  nearest  approach  to  each  other,  so  that  Jupiter's  period  appeared  to 
be  shortened  and  Saturn's  lengthened,  greatly  to  the  perplexity  of 
astronomers,  till  Laplace  demonstrated  the  cause.     Similar  coincidences 
exist  in  the  periods  of  Venus  and  the  earth,  but  the  disturbance  accu- 
mulates only  for  a  short  period.     It  will  be  obvious,  therefore,  that  the 

QTTOSTIONS.— 304.  How  are  the  motions  of  the  planets  accelerated  or  retarded'  ". 
Effect  in  circular  orhits?  In  elliptical  orbits,  6.  Great  inequality  of  Jupiter  and 
Saturn — what  is  meant  hy  it? 


ATTRACTIONS   OF  THE    PLANETS.  207 

stability  of  the  system,  since  the  orbits  are  not  circular,  depends  on  the 
periods'  being  incommensurable. 

305.  Since  the  attraction  of  gravitation  is  reciprocal,  the 
sun  is  attracted  by  the  planets,  and  each  primary  planet  is 
attracted  by  its  satellites ;  and,  therefore,  instead  of  revolv- 
ing one  around  the  other  as  a  centre,  they  in  fact  revolve 
around  their  common  centre  of  gravity. 

a.  By  the  centre  of  gravity  of  two  or  more  bodies  connected  together 
in  any  way,  is  meant  the  point  around  which  they  all  balance  eacii 
other.  The  centre  of  gravity  of  the  solar  system  moves  in  a  small 
and  very  irregular  orbit,  since  it  results  from  the  joint  action  of  all  the 
planets  Its  distance  from  the  centre  of  the  sun  can  never  be  equal  to 
the  diameter  of  the  latter  ;  and  within  this  limit  the  centre  of  the  sun 
must  revolve  around  it. 

306.  MASSES  OF  THE  PLANETS.— The  amount  of  attrac- 
tion exerted  by  one  body  upon  another  is  an  exact  measure 
of  its  mass.    The  masses  of  the  planets  that  are  attended 
by  satellites  are  found  by  comparing  the  attraction  of  the 
sun  upon  the  planets,  with  the  attraction  which  they  exert 
themselves  upon  their  satellites.     The  masses  of  the  planets 
not  attended  by  satellites  are  found  by  ascertaining  the 
amount  of  disturbance  which  they  occasion  in  the  motions 
of  bodies  in  their  vicinity. 

a.  Comparative  Masses  of  the  Sun  and  Planets. — To  determine 
these  it  will  be  most  convenient  to  resort  to  simple  algebraic  represen- 
tation. Let  M  be  the  mass  of  the  sun,  and  ra  that  of  the  earth  ;  F  and 
/,  their  respective  forces  of  attraction,  P  and  p,  their  periodic  times, 
and  D  and  d,  their  distances.  Then,  according  to  the  law  of  gravita- 
tion, the  ratio  of  the  attractions  is  equal  to  the  direct  ratio  of  the 
masses  multiplied  by  the  inverse  ratio  of  the  squares  of  the  distances. 

That  is,  -  =  —  X  ^  ;  hence,    (dividing  by  —  ^   we  have  —  =  -  x 

QUESTIONS.— 305.  Do  the  planets  revolve  around  the  sun  as  n  centre t  a.  What  is 
meant  by  the  centre  of  gravity  ?  What  is  the  shape  and  magnitude  of  the  sun's  orbit, 
and  the  orbit  of  the  centre  of  gravity  ?  306.  What  is  the  general  method  of  determin- 
ing the  masses  of  the  planets  ?  a.  How  to  find  the  comparative  masses  of  the  sun  and 
planets  ?  What  calculation  is  made  for  the  sun  and  earth  ?  The  earth  and  Saturn  ? 


208  ATTRACTIONS    OF    THE    PLANETS. 

D3 

-=-  .    But  it  can  be  shown  by  simple  geometry  that  the  forces  are 

directly  as  the  distances  and  inversely  as  the  squares  of  the  periodic 

TT         T^          /nl  \l"          T^3 

times.      That  is,  -  =  -  x  —  •     Therefore  by  substitution,    —  =  — 
/  '      d      P8  m      d* 

X  |ij  ;  that  is,  the  ratio  of  the  masses  is  equal  to  the  direct  ratio  of  the 

cubes  of  the  distances  multiplied  by  the  inverse  ratio  of  the  squares  of  the 
periodic  times.  ^Hence  the  muss  oi  the  sun  (that  of  the  earth  being  one)  is 


tion,  we  take  no  account  of  the  attraction  of  the  earth  upon  the  sun 
or  of  the  moon  upon  the  earth  ;  but  this  is  so  small  that  it  would 
not  affect  the  result  materially. 

The  above  formula  is  applicable  to  the  case  of  any  planet  that  is 
attended  by  satellites.  Thus,  the  masses  of  the  earth  and  Saturn  may 
be  compared  by  the  periodic  times  and  distances  of  the  moon  and  any 
of  the  satellites  of  Saturn.  The  distance  of  Dione  is  245,846  miles,  and 
its  periodic  time  about  66  hours  ;  hence  the  cube  of  the  ratio  of  the 
distance  of  this  satellite  and  tliat  of  the  moon  multiplied  by  the 
square  of  the  ratio  of  their  periodic  times,  or  (Hf  t-JS)8  X  (^)5,  will 
give  the  mass  of  Saturn,  the  earth  being  1  By  performing  the  work 
the  result  will  be  found  to  be  89  -f,  which  is  very  nearly  correct. 

The  mass  of  the  sun  as  compared  with  the  earth  can  also  be  found 
by  finding  the  force  of  gravity  at  the  surface  of  the  earth  and  compar- 
ing it  with  the  force  of  the  sun  upon  the  earth,  as  determined  by  the 
distance  and  orbital  velocity  of  the  latter. 

T)3       TVT       P^ 
b.  From  the  third  of  the  above  formulae  it  is  obvious  that  -^  =  —  X  -5 

and  this  is  evidently  applicable  to  planets  revolving  around  the  same  cen- 

•vr 

tral  body.  But  in  that  case,  the  mass  being  the  same,  —  becomes  equal 

D3       P* 
to  1  ;  and,  therefore,-^  =  —  9  ;  that  is,  the  squares  of  the  periodic 

times  are  in  propm'tion  to  the  cubes  of  the  mean  distances  ;  which  is 
Kepler's  great  law. 

QTTESTION.-6.  What  demonstration  of  Kepler's  third  law  is  given? 


CHAPTER   XVI. 

COMETS. 

307.  COMETS  are  bodies  of  a  nebulous  or  cloudy  appear- 
ance  that  revolve  around  the  sun  in   very  eccentric   or 
irregular  orbits,  and  are  generally  accompanied  by  a  long 
and  luminous  train,  called  the  tail 

308.  They  generally  consist  of  three  parts ;  the  nucleus, 
or  bright  and  apparently  solid  part  in  the  centre  ;  the  coma, 
or  nebulous  substance  which  envelops  it;    and  the  tail, 
which  extends  on  the  side  from  the  sun. 

a.  The  name  comet  is  derived  from  this  nebulous  appearance  which 
the  ancients  fancifully  likened  to  hair  [in  the  Greek,  come],  and  hence 
called  these   bodies  eometce,  or  hairy  bodies.     When  the  luminous  train 
precedes  the  comet,  it  is  sometimes  called  the  Icard. 

b.  The  appearance  of  comets  is  not  uniform,  the  same  comet  chang- 
ing" very  much   at  different  times.     Some  comets  have  no  nucleus, 
others,  no  tails ;  while  still  others  have  several  tails. 

c.  These  bodies  when  at  a  long  distance  from  the  earth  and  sun  are 
distinguished  from  planets  by  the  size  and  position  of  their  orbits,  and 
the  direction  of  their  motions.     Uranus,  it  will  be  remembered,  was 
for  some  time  thought  to  be  a  comet,  and  was  recognized  as  a  plane 
tary  body  only  after  its  orbit  had  been  proved  to  be  almost  circular,  and 
nearly  in  the  plane  of  the  ecliptic. 

309.  Comets  either  revolve  around  the  sun   in  elliptic 
orbits,  or  move  in  curve  lines  called  by  mathematicians  para- 
lolas  and  hyperbolas.     Elliptic  comets  may  be  considered  as 

QTIFSTIONS.— 30T.  What  are  cornets?  308.  Of  what  parts  do  they  consist?  a. 
Origin  of  the  name  6.  Is  the  appearance  of  a  comet  uniform  ?  c.  How  distinguished 
from  planets  ?  809.  In  what  kind  of  orbits  do  they  revolve  ? 


210 


COMETS. 


belonging  to  the  solar  system ;  the  others,  only  as  visitants 
of  it,  since  they  come  from  distant  regions  of  space,  move 
around  one  side  of  the  sun,  and  then  pass  swiftly  away  in 
paths  that  never  return  into  themselves,  but  are  constantly 
divergent. 

D'ig.  liO. 


OBBITS   OF   COMETS. 

a.  These  paths  are  curve  lines  of  peculiar  properties ;  they  are  called 
"  conic  sections,"  because  they  may  be  formed  by  cutting  a  cone  in 
various  ways.  Thus,  if  a  cone  be  cut  by  a  plane  parallel  to  its  base 
the  curve  formed  will  be  a  circle;  if  both  sides  of  the  cone  be  cut 
obliquely  by  a  plane,  the  curve  will  be  an  ellipse ;  both  of  these  curves 
are  continuous  lines,  returning  into  themselves.  But  if  the  cone  be 
cut  by  a  plane  parallel  to  either  side  and  intersecting  the  base,  the  curve 
formed  will  be  a  parabola  ;  and  if  a  plane  be  passed  through  the  cone 
so  as  to  intersect  the  base  at  an  angle  greater  than  that  of  the  plane 
of  the  parabola,  the  resulting  curve  will  be  a  hyperbola.  The  parabola 
and  hyperbola  are  not  continuous  but  divergent  curves ;  hence  they 
do  not  return  into  themselves.  The  parabola  is  like  an  ellipse  with 
only  one  focus,  or  an  eccentricity  infinitely  great ;  and  when  only  a 

QUESTION— «.  Conic  sections? 


COMETS.  211 

portion  of  it  is  given,  it  is  very  difficult  to  distinguish  h  from  an  ellipse. 
The  hyperbola  is  more  easily  distinguished,  because  its  arms  or  branches 
are  more  divergent. 

In  Fig.  110  these  three  kinds  of  paths  are  represented;  A  and  P  being  the 
aphelion  and  perihelion  of  an  elliptic  orbit ;  a  P  6,  the  two  branches  of  a  para- 
bolic path  ;  and  e  P  d,  those  of  a  hyperbolic  path.  The  greater  divergency 
of  the  last  will  be  obvious;  also,  that  the  elliptic  and  parabolic  curves  coincide 
from  1  to  2,  so  as  to  be  entirely  undistinguishable.  The  motion  indicated 
by  the  arrows  is  direct. 

310.  The  ELEMENTS  of  a  comet's  orbit  are,  1.  The  longitude 
of  the  perihelion  ;  2.  The  longitude  of  the  ascending  node ; 
3.  The  inclination  to  the  plane  of  the  ecliptic  ;  4.  The  eccen- 
tricity ;  5.  The  direction  of  the  motion;   6.  The  perihelion 
distance  from  the  sun. 

311.  The  elements  of  more  than  240  cometary  orbits  have 
been  computed ;  and  of  these  only  19  are  known  to  be  elliptic, 
and  5  hyperbolic.    The  remainder  are  either  parabolic,  or 
elliptic  of  very  great  eccentricity. 

a.  Besides  the  19  elliptic  comets  mentioned,  there  are  37  that  are 
believed  to  be  elliptic  although  they  have  not  been  proved  to  be  so ; 
and  11  others  more  doubtful.  There  are  also  10  doubtful  hyperbolic 
comets ;  leaving,  out  of  242  comets  whose  elements  have  been  com- 
puted, 160  with  parabolic  orbits,  or  orbits  having  an  eccentricity  too 
great  to  be  ascertained  with  accuracy. 

312.  The  ELLIPTIC  COMETS  are  divided  into  two  classes  ; 
those  of  short  periods  and  those  of  long  periods.    The  for- 
mer are  seven  in  number,  and  have  all  reappeared  several 
times,  their  identitv  being  satisfactorily  established  by  an 
entire  correspondence  of  their  elements.     The  most  noted  • 
of  these  is  the  comet  of  Encke,  the  period  of  which  is  about 
3|  years,  eighteen  returns  of  it  having  been  recorded. 

a.  The  others  are  De  Vice's,  the  period  of  which  is  5£  years ;  Win- 
necke's,  5$  years  ,  Br or sen's,  5%  years ;  Biela's,  6|  years  ;  D' Arrest' 8, 

QUESTIONS.— 310.  What  are  the  elements  of  a  comet's  orbit?  311.  How  many  have 
been  calculated  ?  «.  Different  kinds  of  orbits  ?  312.  Classes  of  the  elliptic  comet*  ?  a. 
Which  are  of  short  period  ? 


COMETS. 

6f  years ;  Faye's,  7£  years.  These  comets  are  named  after  the  distin- 
guished astronomers  who  first  discovered  them,  or  determined  their 
periods  and  predicted  their  returns.  Several  others  are  thought  to  be 
comets  of  short  periods. 

b.  These  comets  have  comparatively  small  orbits,  the  mean  distance 
of  each  being  less  than  that  of  Jupiter,  and  all  revolving  within  the 
orbit  of  Saturn.  The  inclination  of  the  orbits  is  comparatively  small, 
the  average  being  about  12£°.  The  greatest  is  31°,  and  the  least  3°. 
They  all  revolve  from  west  to  east.  They  are  not  conspicuous  objects, 
but  have  been  generally  visible  only  with  the  aid  of  a  telescope. 

313.  With  the  exception  of  a  few  comets,  the  periods  of 
which  have  been  computed  to  be  about  75  years,  all  the 
remaining  elliptic  comets  are  thought  to  be  of  very  long 
periods,  some  more  than  100,000  years. 

a.  The  comet  of  1744  is  estimated  to  require  nearly  123,000  years 
to  complete  one  revolution  ;  that  of  1844,  102,000  years ;  and  the  great 
comet  of  1680,  about  9,000  years.  The  period  of  a  comet  can  not,  how- 
ever, be  ascertained  with  precision  during  one  appearance,  since  only 
a  very  small  part  of  its  orbit  is  described  during  the  short  time  it 
remains  visible.  There  is,  consequently,  considerable  uncertainty  in 
these  determinations.  To  the  great  comet  of  1811,  the  two  periods  of 
2,301  and  3,065  years  have  been  assigned. 

314.  Of  all  the  comets  whose  orbits  have  been  ascertained, 
about  one-half  are  direct,  that  is,  revolve  from  west  to  east ; 
the  remainder  are  retrograde.     Their  inclinations  are  very 
diverse,  some  revolving  within  the  zodiac,  others  at  right 
angles  with  the  ecliptic. 

a.  There  is  a  decided  tendency  in  the  periodic  comets  to  revolve  in 
orbits  but  little  inclined  to  the  ecliptic ,  while  the  greatest  number  of 
comets  are  found  moving  in  or  near  a  plane  inclined  50°  to  the  ecliptic. 
Most  of  the  elliptic  and  hyperbolic  comets  are  direct;  of  the  parabolic, 
retrograde. 

6.  About  three-fourths  of  all  the  comets  have  their  perihelia  within 
the  orbit  of  the  earth  ;  and  nearly  all  the  others,  within  the  orbit  of 

QUESTIONS.— ft.  Size  and  inclination  of  the  orbits  ?  313.  Comets  of  long  period  ?  a. 
•Examples  ?  814.  Direction  of  the  motion  of  comets  ?  a.  Tendencies  of  the  periodic 
comets  ?  6.  Situation  of  the  perihelia?  Aphelia  ?  How  found  ? 


COMETS.  213 

the  nearest  asteroid.  Only  one  is  situated  more  than  400,000,000 
miles  from  the  sun.  Some  comets,  on  the  other  hand,  come  into  close 
proximity  to  the  sun.  The  great  comet  of  1680  approached  within 
600,000  miles  of  it ;  and  that  of  1843  was  less  than  75,000  miles.  The 
aphelion  distances  of  some  of  these  comets  are  inconceivably  great. 
The  comet  of  1811  recedes  to  a  distance  from  the  sun  equal  to  14  times 
that  of  Neptune,  or  more  than  40,COO  millions  of  miles  ;  the  greatest 
known  (that  of  1844)  must  be  nearly  400,000  millions  of  miles. 

The  aphelion  distance  can  be  found  from  the  eccentricity  and  peri- 
helion distance.  The  latter  in  the  case  of  the  comet  of  1844  is  about 
80,000,000  miles  ;  the  eccentricity,  .9996  of  the  semi-axis.  Hence  1  — 
.9996  —.0004  of  the  semi-axis  must  be  the  perihelion  distance;  and 
80,000,000 -r-  .0004  =  200,000,000,000  =  semi-axis. 

c.  The  velocity  of  comets  as  they  move  through  their  perihelia  is 
amazingly  great.  That  of  1680  was  880,000  miles  an  hour ;  and  that 
of  1843,  about  1,260,000  miles  an  hour,  or  350  miles  per  second.  The 
latter  body  swept  around  the  sun  from  one  side  to  the  other  in  about 
two  hours. 

315.  The  NUMBER  OF  COMETS  is  supposed  to  be  very  great. 
From  the  earliest  period  up  to  the  present  time  more  than 
800  have  been  recorded,  of  which  nearly  300  have  had  their 
orbits  computed,  and  of  the  latter  54  have  been  identified 
as  returns  of  previous  comets. 

a.  Since  it  is  only  within  the  last  100  years  that  optical  aid  has 
been  made  available  in  searching  for  comets,  it  is  supposed  that  the 
actual  number  of  comets  that  have  come  within  view,  in  both  hemi- 
spheres, is  not  less  than  4,000  or  5,000.  M.  Arago  estimates  that  the 
greatest  possible  number  in  the  solar  system  can  not  exceed  350,000. 

316.  The  SIZE  of  comets,  including  both   envelope  and 
nucleus,  very  much  exceeds  that  of  the  largest  planet ;  the 
nucleus  is,  however,  comparatively  small,  the  diameter  of  the 
largest  measured  being  about  8,000  miles  (that  of  1845). 

a.  The  nucleus  of  the  comet  of  1858  (Donati's)  was  5,600  miles  in  diam- 
eter ;  that  of  1811,  only  428  miles.  The  coma  of  the  latter  was  found  to 

QUESTIONS. — c.  Velocity  of  comets?  315.  The  number  of  comets?  a.  Probable 
number  that  have  visited,  or  that  belong  to,  the  system?  316.  Size  of  comets?  a. 
Examples ?  Change  of  size  at  different  times? 


COMETS. 

be  1,125,000  miles  ;  and  that  of  Encke,  281,000  miles.  The  dimensions 
of  comets,  however,  vary  greatly  at  different  parts  of  their  orbits,  con- 
tracting as  they  approach  the  sun,  and  expanding  as  they  recede  from 
it.  Thus  Encke's  comet  in  October,  1838,  was  more  than  250,000  miles 
in  diameter  ;  but  in  December,  contracted  to  3,000  miles. 

317.  The  MASSES  AND  DENSITIES  of  the  comets  must  be 
inconceivably  small;    since,  notwithstanding   their   great 
magnitudes,  they  move  among  the  planets  and  their  satel- 
lites without  in  the  least,  as  far  as  it  can  be  observed, 
affecting  their  motions  ;  although  they  are  themselves  greatly 
disturbed  by  the  attractions  of  the  planets. 

a.  Their  densities  are,  without  doubt,  many  thousand  times  less  than 
atmospheric  air.  Stars  are  seen  very  clearly  through  the  nebulous 
coma  and  train  of  a  comet,  notwithstanding  that  the  light  has  to  pass 
sometimes  through  millions  of  miles  of  the  substance. 

318.  The  TAILS  of  comets  are  often  of  immense  length, 
and  are  generally  of  a  bent  or  curved  form,  extending  on  the 
side  from  the  sun  and  nearly  in  a  line  with  the  radius- 
vector  of  the  orbit.      The  tail  increases  in  length  as  the 
comet  approaches  the  sun,  but  attains  its  greatest  dimensions 
a  short  time  after  the  perihelion  passage,  and  then  gradually 
diminishes. 

a.  In  respect  to  magnitude,  the  tails  of  comets  are  the  most  stupen 
dous  objects  which  the  discoveries  of  astronomers  have  presented  to 
our  contemplation.     That  of  the  comet  of  1680  was  more  than  100,000,- 
000  miles  in  length  ,  while  the  comet  of  1843  presented  a  train 
200,000,000  miles  long,  which  was  shot  forth  from  the  head  of  the 
comet  in  the  incredibly  short  space  of  twenty  days.    The  increase  of 
the  tail  and  the  decrease  of  the  head  of  the  comet  as  it  approaches  the 
sun,  are  among  the  most  striking  phenomena  presented  by  these  bodies 

b.  The  tails  ol  comets  are  not  of  uniform  breadth,  but  diverge  or 
spread  out  as  they  extend  from  the  head.    The  middle  of  the  tail 
usually  presents  a  dark  stripe  which  divides  it  longitudinally  into  two 
parts.     This  appearance  is  usually  explained  by  the  supposition  that 

QUESTIONS.— 31 T.  Masses  and  densities  1  a.  Why  is  the  density  thought  to  he  small  ? 
318.  Position  and  length  of  tails?  a.  Examples?  Change  in  length  at  different  times  f 
b.  Appearance  of  tails  ?  How  explained  ? 


COMETS.  215 

the  tail  is  hollow,  being  a  kind  of  conical  shell  of  vapor ;  and  as  we 
look  through  a  considerable  thickness  of  the  vapor,  at  the  edges,  it 
appears  brighter  there  than  in  the  middle  where  the  quantity  is  com- 
paratively small. 

c.  The  diminution  of  the  size  of  comets  as  they  approach  the  sun  is 
probably  to  some  extent  only  apparent ;  since  their  substance  must 
necessarily  be  vaporized  as  they  approach  the  sun,  and  much  of  it  so 
attenuated  as  to  become  invisible.  There  is  no  doubt  also  that  a  consid- 
erable portion  is  exhausted  in  the  formation  of  the  tail ;  and  that  as 
the  comet  moves  in  its  orbit  it  loses  by  disruption  considerable  portions 
which  pass  away  into  space. 

319.  Observations  with  the  polariscope  have  shown  that 
the  tails  of  comets  shine  by  reflected  light ;  but  that  the 
nucleus  and  coma  emit  quite  a  strong  radiance  of  their  own. 

a.  If  the  head  of  the  comet  shone  by  reflected  light  alone,  its  appar- 
ent brightness  would  be  inversely  proportional  to  the  product  of  the 
squares  of  the  distances  from  the  sun  and  earth  ;  but  this  is  contrary 
to  observation.     Donati's  comet  (that  of  1858),  according  to  this  rule, 
should  have  been  188  times  as  bright  when  near  its  perihelion  in  Octo- 
ber as  it  was  in  June  ;  whereas  it  was  actually  6,300  times  as  bright,  its 
own  light  having  increased  in  the  ratio  of  33  to  1. 

b.  Some  astronomers  suppose  the  nucleus  to  be  a  solid,  partially  or 
wholly  converted  into  vapor  by  the  intense  heat  of  the  sun  ;  others, 
that  it  is  of  the  same  nature  as  the  coma,  only  more  dense.     It  was  the 
opinion  of  Sir  William  Herschel,  and  is  still  a  very  generally  accepted 
one,  that  the  nucleus  is  surrounded  with  a  transparent  atmosphere  of 
vast  extent,  within  which  the  nebulous  envelop  floats  like  clouds  in 
the  earth's  atmosphere.      This  nebulous  matter  appears  to  be  con- 
tinually driven  off  by  some  force  emanating  from  the  sun,  and  thus 
f  rms  the  luminous  train.     At  their  perihelia  comets  must  generally 
be  subjected  to  a  heat  far  more  intense  than  would  be  required  to  melt 
the  hardest  substance  found  on  the  surface  of  the  earth.     Prof.  Norton 
thinks  that  the  tail  is  formed  by  two  streams,  in  opposite  magnetic  or 
electric  states,  expelled  from  opposite  points,  or  poles,  of  the  nucleus, 
and  bent  back  by  the  sun's  repulsive  force  until  they  nearly  meet,  being 
separated  by  only  a  narrow  interval,  which  appears  as  the  dark  stripe 
noticed  in  the  tail. 

QUESTIONS. — c.  Change  in  the  size  of  comets — how  explained  ?  810.  Are  comets  self- 
luminous  ?  a.  Why  thought  to  be  so  ?  &.  Nature  of  the  nucleus  and  the  tail  ? 


216  COMETS. 

HEMARKABLE    COMETS. 

320.  COMET  OF  1680. — This  was  the  comet  that  Newton 
subjected  to  the  calculations  by  which  he  showed  that  these 

Fig.  lu.  bodies  revolve  in 

one  of  the  conic 
sections,  and  that 
they  are  retained 
in  their  orbits  by 
the  same  force 
that  binds  the 
planets  to  the 
sun.  It  was  very 
GBEAT  OOMET  OF  1680.  remarkable  for 

its  splendor,  and  for  the  extent  of  its  train,  which  stretched 
over  an  arc  of  70°  in  the  heavens,  and  reached  the  amazing 
length  of  120,000,000  miles.  With  the  exception  of  the 
comet  of  1843,  it  approached  nearer  to  the  sun  than  any 
other  known,  and  moved  through  its  perihelion  with  a 
velocity  of  880,000  miles  an  hour. 

a.  Its  perihelion  distance  is  .0062  (the  earth's  distance  being  1),  and 
its  eccentricity,  according  to  Encke,  is  .99998  Now,  91,500,000  X 
.0062  =  567,300 ;  and  1  —  .99998  =  .00002.  Hence  567,300  -i-  .00002  = 
28,365,000,000,  which  is  its  semi  axis;  and  if  we  multiply  this  by  2, 
and  subtract  the  perihelion  distance  from  the  product,  we  shall  find 
the  aphelion  distance,  which  is  equal  to  nearly  57,000  millions  of  miles. 
The  period  corresponding  to  this  orbit  is  8,814  years.  Some  ascribe  to 
this  comet  a  much  shorter  period ;  and  others,  a  hyperbolic  orbit. 

321.  HALLEY'S   COMET.  —  This  comet  derives  its  name 
from   Sir  Edmund   Halley,  a   celebrated   English   astron- 
omer, who  calculated  its  orbit  and  predicted  its  return.     It 
appeared  in  1682,  and  Halley  noticing  a  close  resemblance 

QUESTIONS.— 320.  How  is  the  comet  of  1680  described  ?  a.  Its  distance  and  period  ? 
321.  Halley1  s  comet? 


COMETS. 

in  its  elements  to  those  of  JN* 

1531  and  1607,  concluded 
that  the  comets  of  these 
years  were  different  appear- 
ances of  the  same  comet,  and 
ventured  to  predict  its  re- 
appearance in  1758  or  1759. 
This  prediction  was  real- 
ized by  the  return  of  the 
comet  in  March,  1759;  and 
it  again  appeared  in  1835. 
These  different  appearances,  HAU.RY-B  COMET,  isss. 

it  will  be  observed,  were  about  75  years  apart ;  and  others  of 
an  earlier  date  have  also  been  recognized. 

a.  History   of    the    Prediction.— This   celebrated    prediction  of 
Halley  may  be  considered  almost  the  first  fruits  of  Sir  Isaac  Newton's 
demonstration  of  the  laws  of  planetary  motion  as  contained  in  his 
famous  work,  the  Princlpla.  published  in  1687.     The  comet  of  1682 
had  been  an  object  of  interest  to  both  Halley  and  Newton,  and  its 
path  had  been  calculated  by  Picard,  Flamstead,  and  others,     It  occur- 
red to  Halley  that  this  comet  might  be  identical  with  others  previously 
recorded  ;  and  fortunately  the  comet  of  1607  liad  been  observed  by 
Kepler  and  Longomontanus,  and  that  of  1531,  by  Apian  at  Ingolstadt  j 
the  path  in  each  case  being  quite  accurately  determined.     The  coinci- 
dence which  Halley  noticed  in  these  paths  gave  him  confidence  in  the 
prediction  which  he  made.    He  observed,  however,  that  as  the  comet 
in   the  interval   between    1607    and   1682,  passed    near  Jupiter,  its 
velocity  must  have  been  increased  and  its  period  shortened ;  so  that 
the  next  interval  would  be  76  years  or  upward,  and  the  comet  would 
return  at  the  end  of  1758  or  the  beginning  of  1759.      Subsequent 
researches  gave  increased  force  to  this  prediction  ;  for  it  appeared  that 
comets  had  been  seen  in  1456  and  1378,  whose  paths  seemed  to  have 
been  nearly  identical  with  that  of  the  comet  of  1682. 

b.  The  Prediction  Realized. — As  the  time  drew  near,  the  attention 
of  the  scientific  world  was  awakened  to  the  subject ;   and  it  was 

QUESTIONS. — a.  History  of  the  prediction?    b.  How  was  it  realized? 


218  COMETS. 

resolved  to  compute  more  exactly  the  time  of  the  comet's  appearance, 
by  applying  all  the  additional  resources  of  mathematical  science  that 
seventy-five  years  had  brought  forth.  This  was  a  gigantic  undertaking-, 
since  it  was  necessary  to  calculate  the  distance  of  each  of  the  two 
planets,  Jupiter  and  Saturn,  from  the  comet,  and  the  exact  amount  of 
their  disturbance,  separately,  for  every  successive  degree,  and  for  two 
revolutions  of  the  comet,  or  150  years.  Clairaut  and  Lalande,  two 
French  mathematicians,  undertook  the  work,  the  latter  being  assisted 
in  the  arithmetical  portion  of  it  by  Madame  Lapaute ;  and  after  six 
months  spent  in  calculations,  from  morning  to  night,  this  enormous 
sum  was  worked  out,  and  the  day  of  the  comet's  return  to  its  perihe- 
lion was  announced.  This  was  April  llth.  It  actually  passed  its 
perihelion  March  13th,  or  about  22  days  previously  to  the  predicted 
time  Clairaut,  however,  stated  in  announcing  his  prediction  that  the 
comet  might  be  accelerated  or  delayed  by  the  attraction  of  an  undis- 
covered planet  beyond  the  orbit  of  Saturn,  thus  anticipating,  in 
imagination,  the  discovery  of  Uranus  which  Herschel  made  22  years 
afterward.  Halley  did  not  live  to  witness  the  realization  of  his 
prediction,  having  died  in  1743. 

c.  The  Return  in  1835. — The  time  of  its  perihelion  passage  in 
1835  was  computed  by  several  mathematicians,  the  mean  of  all  the 
results  being  November  12th.     The  comet  was  observed  to  pass  its 
perihelion  on  the  16th  of  that  month.     It  continued  visible  in  the 
southern  hemisphere  for  several  months,  and  then  disappeared,  not  to 
be  seen  again  until  1911. 

d.  The  mean  distance  of  this  comet  is  a  little  less  than  that  of  Uranus. 
Its  perihelion  distance  is  about   60  millions  of  miles;  its  aphelion 
distance  more  than  3,200  millions.     Its  motion  is  retrograde,  and  the 
inclination  of  its  orbit  about   18°.    History  shows  that  it  has  reg- 
ularly returned  during  a  period  of  more  than  18  centuries,  its  first 
recorded  appearance  being  in  11  B.C.     It  seems  however,  to  have  been 
a  far  more  conspicuous  object  in  its  ancient  visitations  than  at  its  more 
recent  returns.     In  1066  and  1456,  it  was  an  object  of  immense  size 
and  splendor,  and  created  wide-spread  alarm. 

322.  ENCKE'S  COMET  is  remarkable  for  its  short  period  and 
frequent  returns.    Its  period  and  elliptic  orbit  were  deter- 

QUESTIONS. — c.  Return  in  1836  ?    d.  Distance,  etc.  ?    322.  Encke's  comet  ? 


COMETS.  219 

mined  by  Professor  Encke  Fis-  H3. 

at  its  fourth  recorded  ap- 
pearance in  1819.  Its 
last  return  took  place  in 
1868 ;  the  next  will  occur 
in  January,  1872.  This 
comet  has  generally  ap- 
peared without  any  lumi- 
nous train ;  but  in  1848, 
it  had  a  tail  about  1° 

long,     turned      from      the  ENCKE' s  COMET. 

sun,  and  a  shorter  one  directed  toward  that  luminary.  In 
its  latest  returns  it  has  been  very  faint  and  difficult  of 
observation. 

«.  Mass  of  Mercury. — The  return  of  1838  led  to  the  establishment 
of  an  important  fact.  In  August,  1835,  this  comet  passed  very  near 
Mercury  ;  and  Encke  showed  that,  if  Laplace's  value  of  Mercury's  mass 
were  correct,  the  comet's  motion  would  be  greatly  disturbed ;  but  as 
this  was  found  not  to  be  the  case,  it  was  obvious  that  the  received 
determination  of  Mercury's  mass  needed  correction.  A  much  lower 
value  has  since  been  adopted  ;  but  astronomers  do  not  entirely  agree 
as  to  this  element.  Encke's  value  is  about  ^  that  of  the  earth ;  but 
Leverrier's  is  a  little  more  than  i1,;.  Laplace's  had  been  about  £. 

b.  The  Resisting  Medium. — A  still  more  interesting  discovery  has 
been  evolved  from  observations  of  this  comet.  Professor  Encke  found 
that  at  each  return,  the  arrival  of  the  comet  at  its  perihelion  took 
place  about  2:|  hours  earlier  than  the  most  exact  calculations  predicted , 
and  that  this  constant  acceleration  had  amounted  since  178G  to  about 
2  j  days.  As  this  could  not  be  attributed  to  the  disturbing  influence  of 
any  unknown  body,  he  conceived  that  it  could  be  caused  only  by  a 
resisting  medium  filling  the  interplanetary  spaces  ;  since  the  effect  of 
such  a  medium  would  be  to  diminish  the  centrifugal  force,  and  thus 
bring  the  body  nearer  to  the  sun  :  so  that  its  orbit  would  be  con. 
tracted  and  its  periodic  time  made  constantly  shorter.  A  very  ethereal 
fluid  would  be  sufficient  to  produce  this  result  in  the  case  of  a  body  so 
light  as  a  comet ;  while  it  would  have  no  appreciable  effect  on  the 

QUESTIONS. — «.  How  was  the  mass  of  Mercury  found  ?    b.  Resisting  medium  ? 


220 


COMETS. 


planets  on  account  of  their  great  mass  and  enormous  momentum.  A 
similar  acceleration  takes  place  in  the  case  of  Faye's  comet. 

323.  LEXELI/S  COMET. — This  body  is  particularly  noted 
for  the  amount  of  disturbance  which  it  has  suffered  in  pass- 
ing among  the  planets.  From  observations  made  in  1770, 
Lexell  calculated  its  period  at  about  5 A  years  ;  and  it  was 
a  large  and  bright  object,  the  diameter  of  its  head  being 
about  2  3°.  It  has,  however,  never  been  seen  since,  its  orbit 
having  been  entirely  changed  by  planetary  disturbance. 

a.  Investigation  showed  that  it  really  returned  in  1776,  but  was  so 
situated  as  to  be  continually  hid  by  the  sun's  rays ;  that  in  1779,  it 
passed  so  near  Jupiter  that  its  orbit  was  greatly  enlarged,  so  that  it  no 
longer  comes  near  the  earth.  The  fact  that  it  never  appeared  previous 
to  1770,  is  accounted  for  in  a  similar  way  ;  its  orbit  having  in  1767  been 
changed  by  the  attraction  of  Jupiter,  from  one  of  large  to  one  of  small 
dimensions.  On  July  1st,  1770,  the  distance  of  this  comet  from  the  earth 
was  less  than  1,500,000  miles. 

324.  COMET  OF  1744.— 
This  was  the  finest  comet 
of  the  18th  century,  and 
according  to  some  ob- 
servers, had  six  tails  spread 
out  in  the  form  of  a  fan. 
Euler  calculated  its  ellip- 
tic orbit,  and  assigned  to 
it  a  period  of  122,683 
years.  Its  motion  was 
direct. 

COMET  OF  n44  325.  BIELA'S  COMET.— 

This  is  one  of  the  elliptic  comets  of  short  period ;  its  perihe- 
lion lying  just  within  the  orbit  of  the  earth,  and  its  aphelion 
a  little  beyond  that  of  Jupiter.  The  orbit  of  this  body 


Fig.  114. 


QUESTIONS.— 323.  Lexell's  comet— why  noted?    er»  How  accounted  for  ?    324.  Comet 
of  1744?    325    Biela'scomet? 


COMETS.  221 

nearly  crosses  the  actual  path  of  the  earth ;  and  in  1832, 
Gibers  calculated  that  it  would  come  within  20,000  miles  of 
the  earth,  so  that  the  latter  body  would  be  enveloped  in  its 
mass.  The  earth,  however,  did  not  reach  the  node  until  one 
month  after  the  comet  had  passed  it. 

a.  In  1845,  this  comet  became  elongated  in  form  and  finally  sepa- 
rated into  two  comets,  which  traveled  together  for  more  than  three 
months ;  their  greatest  distance  apart  being  about  160,000  miles.  The 
two  parts  were  again  seen  at  the  next  return  of  the  comet  in  1852,  but 
the  interval  had  increased  to  1,250,000  miles.  It  has  not  been  seen  since 

Fig.  115. 


COMET  OF  1811. 

326.  COMET  OF  1811.— This   comet  was  very  remarkable 
for  its   unusual   magnitude   and   splendor.     It  was  atten- 
tively observed  by  Sir  William  Herschel,  who  describes  it  as 
having  a  nucleus  428  miles  in  diameter,  which  was  ruddy  in 
hue,  while  the  nebulous  mass  surrounding  it  was  of  a  blu- 
ish-green tinge.    Its  tail  was  of  peculiar  form  and  appearance, 
extending  about  25°,  with  a  breadth  of  nearly  6°. 

n.  The  investigation  of  its  elements  by  Argelander  is  the  most  com- 
plete ever  made  He  assigns  it  a  period  of  more  than  3,000  years,  and 
estimates  its  aphelion  distance  at  40,121  millions  of  miles. 

327.  COMET  OF  1843,-This  comet  was  also  remarkable  for  its 

QUESTIONS.— •«.  Its  separation?  326.  Comet  of  1811  ?  a.  Its  elements  ?  32T.  Comet 
of  1843? 


GREAT   COMET   OF    1843. 

extraordinary  size  and  splendor,  it  being  visible  in  some  parts 
of  the  world  during  the  day  time.  It  had  a  tail  60°  long,  and 
approached  within  a  very  short  distance  of  the  sun, — about 
75,000  miles  from  its  surface.  Its  period  is  variously  esti- 
mated at  from  175  to  376  years.  Its  motion  is  retrograde. 

328.  DONATI'S  COMET.— This  is  the  great  comet  of  1858, 
named  after  Donati,  by  whom  it  was  first  seen  at  Florence. 
As  it  approached  its  perihelion  it  attained  a  very  great  mag- 
nitude and  splendor,  and  was  particularly  distinguished  for 
the  magnificence  of  its  train.     Its  period  has  been  estimated 
at  nearly  1,900  years. 

329.  RECENT   COMETS. — About  thirty  comets  have    ap- 
peared since  that  of  Donati,  the  elements  of  which  have 
been  calculated.     The  most  remarkable  were  the  comet  of 
1861,  described  as  one  of  the  most  magnificent  on  record, 
having  a  tail  100°  long ;  and  that  of  1862,  which  was  very 
interesting  for  the  peculiar  phenomena  which  it  presented 
of  luminous  jets,  issuing  in  a  continuous  series  from  its 
nucleus. 


QUESTIONS  __  328.  Donati'  s  comet? 


Other  comets. 


CHAPTER   XVII. 

METEORS     OB     SHOOTING     STA11S. 

330.  METEORS*  or  SHOOTING  STARS  are  small  luminous 
bodies  that  move  rapidly  through  the  atmosphere,  followed 
by  trains  of  light,  and  quickly  vanishing  from  view.  They 
sometimes  appear  in  numbers  so  great  as  to  seem  like 
showers  of  stars. 

a.  Star-Showers    Periodical. — These  star-showers  are  found  to 
occur  at  certain  periods.     Every  year,  about  November  14th,  there  is 
a  larger  fall  than  usual  of  meteors  ;  but  about  every  33  years,  it  has 
been  noticed,  there  is  a  great  star-shower.     Those  which  occurred  in 
November,  1866-7,  had  been  predicted  from  observations  of  previous 
events  of  the  kind.     Thus  a  star-shower  occurred  in  November,  1832-3, 
also  in  1799 ;  and  there  are  eighteen  recorded  observations  of  the  phe- 
nomena from  1698  to  902,  all  corresponding  in  period  to  that  mentioned 
above. 

b.  Great  Star-Showers.— The  shower  of  1799  was  awful  and  sub- 
lime beyond  conception.     It   was  witnessed  by  Humboldt  and  his 
companion,  M  Bonpland,  at  Cumana,  in  South  America,  and  is  thus 
described  by  them  : — "  Toward  the  morning  of  the  13th  of  November, 
1799,  we  witnessed  a  most  extraordinary  scene  of  shooting  meteors. 
Thousands  of  bolides  and  falling  stars  succeeded  each  other  during  four 
hours.     Their  direction  was  very  regularly  from  north  to  south  ,  and 
from  the  beginning  of  the  phenomenon  there  was  not  a  space  in  the 
firmament,  equal  in  extent  to  three  diameters  of  the  moon,  which  was 
not  filled  every  instant  with  bolides  or  falling  stars.    All  the  meteors 


*  From  the  Greek  word  meteora,  meaning  things  in  the  air. 

QFFBTIOXS.— 330.  What  are  meteors?    a.  What  periods  have  been  observed  in  their 
occurrence  ?    b.  What  instances  of  great  showers  ? 


224  METEORS    OR    SHOOTING    STARS. 

left  luminous  traces,  or  phosphorescent  bands  behind  them,  which 
lasted  seven  or  eight  seconds."  The  same  phenomena  were  witnessed 
throughout  nearly  the  whole  of  North  and  South  America,  and  in  some 
parts  of  Europe.  The  most  splendid  display  of  shooting  stars  on 
record  was  that  of  November  13th,  1833,  and  is  especially  interesting  as 
having  served  to  point  out  the  periodicity  in  these  i-hemmena.  Over  the 
northern  portion  of  the  American  continent  tLe  spectacle  was  of  tli3 
most  imposing  grandeur  ;  and  in  many  \  arts  of  the  country  the  popula- 
tion were  terror-stricken  at  the  awfulness  of  the  scene.  The  ignorant 
slaves  of  the  southern  States  supposed  that  the  wcrld  was  en  fire,  and 
filled  the  air  with  shrieks  of  horror  and  cries  for  mercy.  TLe  shower 
of  1866  was  anticipated  with  great  interest ;  end  in  New  York  and 
other  places  arrangements  were  made  to  announce  the  cccurrence, 
during  the  night  of  November  14th,  by  ringing  the  bells  from  the 
watch-towers.  The  display,  however,  was  not  witnessed  in  this  coun- 
try, but  in  England  was  quite  brilliant ;  as  many  as  8,000  being 
counted  at  the  Greenwich  observatory.  Another  shower  of  less  extent 
occurred  in  November,  1867. 

331.  METEORIC  EPOCHS  are  particular  times  of  the  year 
at  which  large  displays  of  shooting  stars  have  been  observed 
to  occur  at  certain  intervals.     The  principal  of  these  are 
November  13th-14th,  and  August  6th-llth. 

a.  Three  others  have  been  established  with  consielerable  certainty ; 
namely,  in  January,  April,  and  December,  and  still  others  indicated, 
that  are  doubtful.     There  are  56  meteoric  days  in  the  year ;  those  in 
August  and  November  being  the  richest. 

b.  August  Meteors. — Of  315  recorded  meteoric  displays,  63  seem 
to  have  occurred  at  this  epoch.     The  first  eleven,  with  one  exception, 
were  observed  in  China,  between  811  A.D.,  and  933  A.D.,  and  occurred  a 
few  days  previous  to  August  1st.     The  period  of  this  shower  is  exactly 
the  same  as  the  sidereal  year  ,  and  therefore  it  occurs  about  a  day  later 
in  71  tropical  or  civil  years.     Its  maximum  period  is  much  longer  than 
that  of  the  November  meteors,  being  estimated  at  105  years. 

332.  METEORS  are  supposed  to  be  small  bodies  collected  in 

QUESTIONS.— 331.  What  are  the  principal  meteoric  epochs?  a.  What  others?  How 
many  meteoric  days  in  a  year?  b.  August  meteors — dates  of  their  occurrence  and 
periods  ?  332.  What  are  meteors  supposed  to  be  ? 


METEORS    Oil    SHOOTING    STARS.  225 

rings  or  clusters,  and  revolving  around  the  sun  in  eccentric 
orbits.  They  appear  to  resemble  comets  in  their  nature  and 
origin,  and,  liko  those  bodies,  sometimes  revolve  from  cast 
to  west. 

a.  Origin  of  Meteors. — The  immense  velocity  of  these  bodies, 
which  is  about  equal  to  twice  that  of  the  earth  in  its  orbit,  or  86  miles 
a  second,  and  the  great  elevation  at  which  they  become  visible,  the 
average  being  60  miles,  indicate  that  they  are  not  of  terrestrial,  but 
cosmical,  origin  ;  that  is,  they  emanate  from  the  interplanetary  regions, 
and  being  brought  within  the  sphere  of  the  earth's  attraction,  precipi- 
tate themselves  upon  its  surface.  Moving  with  so  great  a  velocity 
through  the  higher  regions  of  the  air,  they  become  so  intensely  heated 
by  friction  that  they  ignite,  and  are  either  converted  into  vapor,  or, 
when  very  large,  explode  and  descend  to  the  earth's  surface  as  mete- 
oric stones,  or  aerolites*  The  brilliancy  and  color  of  meteors  are 
variable  ;  some  are  as  bright  as  Venus  or  Jupiter.  About  two-thirds 
are  white  ;  the  remainder  yellow,  orange,  or  green. 

&.  Number  of  Meteors. — The  average  number  of  shooting  stars 
seen  in  a  clear,  moonless  night  by  a  single  observer  is  8  per  hour  ;  a 
sufficient  number  of  observers  would  perceive  30  per  hour,  which  is 
equivalent  to  720  per  day,  seen  by  the  naked  eye  at  any  point  of  the 
earth's  surface,  if  the  sun,  moon,  and  clouds  were  absent.  But  the 
number  visible  over  the  whole  earth  is  about  10,500  times  that  seen  at 
a  single  point ;  and  therefore  the  average  number  daily  entering  the 
atmosphere,  and  sufficiently  large  to  be  seen  by  the  naked  eye,  is  more 
than  7^  millions ;  while  at  least  50  times  as  many  can  be  seen  through 
the  telescope ;  so  that  about  400  millions  must  descend  to  the  earth 
during  each  day.  It  becomes  therefore  an  interesting  question  how 
much  foreign  matter  may  be  added  to  the  earth  ani  its  atmosphere  by 
these  meteoric  falls. 

333.  FIRE  BALLS  are  large  meteors  that  make  their 
appearance  at  a  great  height  above  the  earth's  surface, 
moving  with  immense  velocity,  and  accompanied  by  luminous 

*From  the  Greek  word  aer,  meaning  the  air,  and  lithos,  a  stone. 

QUESTIONS. — n.  Their  origin?  Cause  of  their  ignition?  Aerolites?  Color  of  me- 
teors? b.  Number  of  meteors?  333.  What  are  fire  balls  ? 


226  METEORS    OH    SHOOTING    STARS. 

trains.     They  generally  explode   with   a   loud  noise,  and 
sometimes  descend  to  the  earth  in  large  masses. 

a.  No  deposit  has  been  known  to  reach  the  earth  from  ordinary 
shooting  stars  ;  probably,  because  being  very  small  they  are  dissipated 
in  the  air  ;  but  scarcely  a  year  passes  without  the  fall  of  aerolites  in 
some  parts  of  the  earth,  either  singly  or  in  clusters.     Some  estimate 
the  whole  number  that  fall  annually  at  700;  others,  much  higher. 
The  most  ancient  fall  of  meteoric  stones  on  record  is  that  mentioned 
by  Livy,  which  occurred  on  the  Alban  Hill,  near  Rome,  about  the  year 
654  B.C.      There  are  very  many  remarkable  occurrences  of  this  kind 
on  record,  some  of  the  masses  being  of  immense  size,  and  the  explo- 
sion so  violent   as  to   sound  like   thunder.     In   1783   a  fire  ball  of 
extraordinary  magnitude  was  seen  in  Scotland,  England,  and  France. 
It  produced  a  rumbling  sound  like  distant  thunder,  although  its  height 
was  50  miles  when  it  exploded.     Its  diameter  was  estimated  at  about 
half  a  mile,  and  its  velocity  was  as  great  as  that  of  the  earth  in  its  orbit. 
In  1859,  between  9  and  10  o'clock  A.M.,  a  meteor  of  immense  size  was 
seen  in  the  eastern  part  of  the  United  States.     Its  apparent  diameter 
was  nearly  equal  to  that  of  the  sun  ;  and  it  had  a  train  several  degrees 
in  length,  plainly  visible  in  the  sunshine.     Its  disappearance  on  the 
coast  of  the  Atlantic  was  followed  by  several  terrific  explosions.     Some 
of  these  meteors  have  been  supposed  to  pass  the  earth,  moving  away 
into  space ;  others  to  revolve  in  an  orbit  around  it,  becoming  small 
satellites.     A  French  astronomer  assigns  to  one  of  the  latter  a  period  of 
revolution  of  3  hours  and  20  minutes,  and  a  distance  from  the  earth  of 
5,000  miles. 

b.  Composition  and  Size  of  Aerolites.— The  materials  composing 
these  bodies  are  always  nearly  the  same,  consisting  largely  of  iron, 
and  in  no  case  of  any  other  elementary  substances  than  are  found  on 
the  earth.     Some  have  been  discovered  of  immense  size  ;  one,  a  mass 
of  iron  and  nickel,  found  in  Siberia,  weighs  1,680  Ibs.    At  Buenos  Ayres 
there  is  a  mass  partly  buried  in  the  ground  7.^  feet  in  length,  and  sup- 
posed to  weigh  about  sixteen  tons.     A  similar  block,  weighing  about 
six  tons,  was  discovered  a  few  years  ago  in  Brazil.    Many  others  exist. 
All  these  are  doubtless  of  cosmical   origin,  having  been  very  small 

QUESTIONS. — a.  Frequency  of  the  fall  of  aerolites?  Earliest  recorded  instance? 
Remarkable  instances  ?  Do  they  all  reach  the  earth?  It.  Composition  of  aerolites? 
Their  size  ?  Additions  to  the  earth,  Venus,  and  Mercury  from  this  cause  ?  Effect  on 
Mercury's  period? 


METEORS    OB    SHOOTING    STARS.  227 

planets  revolving  around  the  sun,  but  brought  within  the  earth's 
attraction  ;  and  there  is  no  doubt  that,  before  the  solar  system  had 
reached  its  present  condition,  the  additions  made  to  the  matter  of 
the  earth  in  this  way  were  quite  considerable.  This  is  supposed 
still  to  be  the  case  with  Venus  and  Mercury,  moving  as  they  are 
through  the  thicker  portions  of  the  great  ling  which  we  call  the 
zodiacal  light.  Now,  as  Mercury's  orbit  is  very  eccentric,  it  receives  at 
its  aphelion  a  large  number  of  these  meteors  whose  periods  are  longer 
than  its  own ;  and  this  would  have  the  effect  to  diminish  its  mean 
motion  and  lengthen  its  period.  Such  an  effect  has  actually  been 
discovered. 

c.  Meteoric  Dust,  etc. — There  are  oa  record  many  instances  of 
showers  of  dark -colored  dust,  which  have  fallen  from  the  higher 
regions  of  the  atmosphere,  and  which  seem  from  the  composition  of 
the  dust  to  be  of  meteoric  origin.  These  falls  are  often  preceded  or 
attended  by  a  flashing  of  light  as  well  as  by  a  loud  noise,  sometimes 
resembling  thunder.  In  March,  1813,  a  shower  of  red  dust  fell  in 
Tuscany,  discoloring  the  snow  which  then  lay  on  the  ground  ;  and  at 
the  same  time,  a  few  miles  distant,  there  occurred  a  shower  of  aero- 
lites, lasting  about  two  hours,  and  accompanied  by  a  noise  as  of  the 
dashing  of  waves  The  phenomena  of  Hack  and  red  rain  and  snow  are 
attributed  to  a  similar  cause.  Since,  as  has  been  shown,  several  mil- 
lions of  meteors  pass  into  the  atmosphere  during  the  year,  there  is  no 
doubt  that  large  quantities  of  dust,  too  fine  to  be  visible,  descend  to 
the  earth's  surface.  Some  of  this  dust  has  been  detected  upon  the 
tops  of  mountains  in  soil  which  had  never  been  previously  disturbed 
by  man.  Partial  obscurations  of  the  sun's  light,  occasioning  what  are 
recorded  as  dark  days,  and  the  passage  of  large  black  masses  across 
the  sun's  disc,  too  rapid  to  be  spots,  are  probably  meteoric  phenomena. 

334.  The  NOVEMBER  METEORS  are  supposed  to  revolve 
around  the  sun  in  an  orbit  of  considerable  eccentricity, 
inclined  to  the  plane  of  the  ecliptic  in  an  angle  of  17^°, 
and  extending  at  its  aphelion  somewhat  beyond  the  orbit  of 
Uranus,  its  perihelion  being  very  nearly  at  that  of  the  earth. 
They  move  in  a  ring  of  unequal  width  and  density,  the 


QUESTIONS.— c.  Showers  of  dust  ?    Black  and  red  rain  ?    334.  Orbit  of  the  November 
meteors  ?    Why  visible  only  every  33  years? 


228  METEORS    OB    SHOOTING    STABS. 

thickest  part  crossing  the  earth's  orbit  every  33  years,  and 
requiring  nearly  two  years  to  complete  the  passage. 

a.  The  elements  of  this  orbit  correspond    almost  precisely  with 
those  of  the  comet  which  made  its  appearance  in  January,  1866 ;  so 
that  it  seems  probable  that  the  comet  is  a  very  large  meteor  of  the 
November  stream.     The  elements  of  the  orbit  of  the  August  meteors 
have  been  found,  in  a  similar  manner,  to  coincide  with  those  of  the 
third  comet  of  1862  ;  showing  that  the  comet  and  these  meteors  belong 
to  the  same  ring.     This  seems  also  to  be  true  of  the  first  comet  of 
1861  and  the  April  meteors. 

b.  The  point  from  which  the  November  meteors  seem  to  radiate  is 
in  the  constellation  Leo ;  because,  as  the  earth  at  that  time  of  the  year 
is  moving  toward  that  point,  they  appear  to  rush  from  it.     Their  veloc- 
ity appears  to  be  double  that  of  the  earth,  although  only  equal  to  it ; 
because  they  move  in  an  opposite  direction  and  almost  in  the  same 
plane.     When  the  earth  plunges  into  the  meteoric  stream  a  great  star- 
shower  occurs. 

c.  Physical  Origin. — Meteors  are  supposed  by  some  to  be  small 
fragments  of  nebulous  matter  detached  in  vast  numbers  from   the 
larger  masses  which  are   seen  in  the  regions  of  the  stars,  or  from 
that  of  which  the  solar  system  was  originally  formed,  tlieir  origin 
being  precisely  the  same  as   that  of  the  comets,  which  indeed  may 
be  considered  as,  in  reality,  only  meteors  of  vast   size.     It  is  also 
probable    that,  like  Biela's    comet,   others  have   been  divided  and 
subdivided  so  as  finally  to  be  separated  into  small  fragments  moving 
in  the  orbit  of  the  original  comet,  and  thus  constituting  a  meteoric 
ring  or  stream. 

d.  The  following  general  conclusions  with  regard  to  meteors  in  the 
solar  system  have  been  suggested :  1.  Biela's  comet  in  1845  passed  very 
near,  if  not  through,  the  November  stream,  and  was  probably  divided 
in  this  way  ;  2.  The  rings  of  Saturn  are  dense  meteoric  streams,  the 
principal  or  permanent  division  being  due  to  the  disturbing  influence 
of  the  satellites ;  3.  The  asteroids  are  a  stream  or  ring  of  meteors, 
the  largest  being  the  minor  planets  which  have  been  discovered ;  4. 
The  meteoric  masses  encountered  by  Encke's  comet  may  account  for 
the  shortening  of  the  period  of  the  latter  without  the  hypothesis  of  a 
resisting  medium. 

QUESTIONS. — a.  Resemblance  to  comets  ?  ft.  Radiant  point  of  November  meteors  ? 
c.  Physical  origin  of  the  meteors  ?  d.  Generalizations  with  regard  to  meteors  in  the 
solar  system  ? 


CHAPTER   XVIII. 

THE   STARS. 

335.  The  STARS  are  luminous  bodies  like  the  sun,  out 
situated  at  so  vast  a  distance  from  the  earth  that  they  seem 
like  brilliant  points,  and  always  in  nearly  the  same  positions 
with  respect  to  each  other. 

a.  The  scintillation  or  twinkling  of  the  stars  is  due  to  the 
inequalities  in  density,  moisture,  etc.,  of  the  different  strata  of  the 
atmosphere  through  which  the  rays  of  light  pass.  In  tropical  regions, 
where  the  atmospheric  strata  are  more  homogeneous,  this  scintillation 
is  rarely  observed ;  so  that,  as  remarked  by  Humboldt,  "  the  celestial 
vault  of  these  countries  has  a  peculiarly  calm  and  soft  character." 

6.  Parallax  of  the  Stars. — The  usual  method  of  finding  the  par- 
allax of  a  body  by  viewing  it  at  different  parts  of  the  earth's  surface 
is  entirely  useless  in  the  case  of  the  stars,  as  the  displacement  thus  occa- 
sioned in  the  positions  of  any  of  them  is  utterly  inappreciable  ;  the 
radius  of  the  earth  at  a  distance  so  immense  being  practically  but  a 
mathematical  point.  If,  however,  we  view  the  same  star  at  intervals 
of  six  months,  our  stations  of  observation  will  be  about  180  millions 
of  miles  apart ;  and  the  amount  of  displacement  thus  occasioned,  when 
reduced  to  the  centre  of  the  orbit,  is  the  stellar  parallax,  called  some- 
times the  annual  parallax. 

336.  The  ANNUAL  PARALLAX  is  the  change  which'  would 
take  place  in  the  position  of  a  star  if  it  could  be  viewed 
from  the  centre  of  the  orbit,  instead  of  the  orbit  itself. 

a.  In  other  words,  it  is  the  angle  subtended  by  the  semi-axis  of  the 


QUESTIONS.— 335.  What  are  the  stars?    ft.  Cause  of  the  scintillation  ?    ft.  Parallax  of 
the  etars,  how  found ?    386.  How  is  annual  parallax  defined?    a.  Greatest  parallax ? 


230  THE    STAKS. 

earth's  orbit  at  the  distance  of  the  star.  The  greatest  parallax  yet 
discovered  in  the  case  of  any  star  is  somewhat  less  than  1"  (0.9187"), 
BO  that  the  earth's  orbit  itself  is  but  little  more  than  a  mere  point  at 
the  nearest  star.  To  determine  this  small  parallax  exactly  is  prob- 
ably the  most  difficult  problem  in  practical  astronomy. 

b.  Distance  Calculated.— The  sine  of  0.9187"  is  about  .000004464, 
which  is  the  ratio  of  the  semi-axis  of  the  earth's  orbit  to  the  distance 
of  the  star.  Hence  the  distance  of  the  star  must  be  224,000  times  the 
semi-axis  of  the  earth's  orbit,  or  91£  millions  of  miles  ;  and  91,500,000 
X  224,000  —  20,496,000,000,000  miles,  or  nearly  20^  trillions  of  miles. 
Light,  moving  with  a  velocity  of  184,000  miles  a  second,  requires  more 
than  3^  years  to  pass  across  this  enormous  interval, — an  interval  more 
than  7,000  times  the  distance  of  Neptune  from  the  sun.  However 
large  the  stars  may  be,  therefore,  their  attraction  upon  the  solar  system 
must  be  altogether  too  feeble  to  disturb  the  motions  cf  its  component 
bodies  in  the  least.  The  parallax  of  twelve  stars  has  been  determined 
with  considerable  precision,  the  smallest  being  0.046 ',  cr  about  one- 
twentieth  that  mentioned  above ;  this  star  must  therefore  be  about 
410  trillions  of  miles  from  us, — a  distance  which  light  would  not  traverse 
in  less  than  70.3  years. 

337.  MAGNITUDES. — The  stars  are  divided  into  classes 
according  to  their  apparent  brightness,  the  brightest  being 
distinguished  as  stars  of  the  first  magnitude,  the  next  of  the 
second,  and  so  on.  Stars  of  the  first  six  magnitudes  are  visi- 
ble to  the  naked  eye  ;  but  the  telescope  reveals  the  existence 
of  others  so  feeble  in  light  as  to  be  classed  as  of  the  seven- 
teenth magnitude. 

a.  This  classification  is  based  exclusively  on  appearance,  and  indi- 
cates nothing  as  to  the  real  magnitudes  of  the  bodies  in  question.  Sir 
John  Herschel  gives  the  following  comparative  estimate  of  the  amount 
of  light  emitted  by  stars  of  the  first  six  magnitudes  : 

6th  magnitude     —     1  3d  magnitude     =     12 


5th  =    2 

4th          «  =6 


2d  =     25 

1st        "  =100 


QUESTIONS. — b.  Distance  of  the  stars,  how  calculated  ?  Of  how  many  stars  hag 
the  parallax  been  found?  The  least?  337.  Magnitudes  of  the  Ftars  ?  How  many? 
«.  What  does  mag  :itude  indicate?  Comparative  brilliancy  of  each  ? 


THE    STABS.  231 

This  is  not  uniformly  the  relative  brightness  of  stars  thus  denominated ; 
Sirius,  the  brightest  star  in  the  heavens,  being  324  times  as  brilliant  as 
an  average  star  of  the  6th  magnitude. 

338.  The  WHOLE  NUMBER  of  stars  visible  to  the  naked 
eye  in  the  northern  hemisphere  is  about  2,400;  in  both 
hemispheres,  more  than  4,500. 

a.  These  are  distributed  by  Argelander  according  to  their  magni- 
tudes as  follows :  1st  magnitude,  9  ;  2d,  34 ,  3rd,  96  ;  4th,  214 ;  5th, 
550  ;  6th,  1439  ;  total  in  northern  hemisphere,  2,342.  If  the  southern 
hemisphere  is  equally  rich  in  stars,  the  whole  number  must  be  4,684  ; 
some  estimate  it  at  6,000  or  7,000.  The  stars  are  probably  less  bright 
in  proportion  as  their  distance  is  greater;  and  hence  the  number 
increases  as  we  descend  to  the  lower  magnitudes.  Argelander's 
estimate  for  the  9th  magnitude  is  142,000.  Viewed  through  the  tele- 
scope, the  stars  can  be  counted  by  millions. 

THE  CONSTELLATIONS. 

339.  To  facilitate  the  naming  and  location  of  the  stars, 
the  heavens  are  divided  into  particular  spaces,  represented 
on  the  globe  or  map  as  occupied  by  the  figures  of  animals 
or  other  objects.      These  spaces  and  the  groups  of  stars 
which  they  contain  are  called  constellations,  or  asterisms. 

a.  Thus  tliere  are  the  constellations  Aries,  the  Ram  ;  Leo,  the 
Lion  ;  Gemini,  the  Twins,  etc.  The  general  position  of  a  star,  accord- 
ing to  this  system,  is  defined  by  stating  in  what  part  of  the  figure  it  is 
situated  ;  as,  the  eye  of  the  Bull,  the  heart  of  the  Lion,  etc.  Its  exact 
position  is,  of  course,  only  to  be  denned  by  its  right  ascension  and 
declination,  or  longitude  and  latitude.  This  system  of  grouping  the 
stars  into  constellations  is  supposed  to  be  very  ancient.  Ptolemy 
counted  only  forty-eight  constellations ;  but,  since  his  time,  the  num- 
ber has  been  augmented  to  109. 

340.  The  stars  belonging  to  each  constellation  are  distin- 
guished by  particular  names ;  as  jSirius,  Regulus,  Arcturus, 
etc.,  and  by  letters  or  numerals. 

QUESTIONS-— 338.  What  number  of  visible  stars?  «.  How  distributed?  339.  Con- 
stellations? a.  How  used  ?  Number  enumerated  by  Ptolemy?  By  modem  astronomers  f 
::4D.  Mode  of  designating  the  stars? 


232 


THE    STAKS. 


a.  Only  the  most  conspicuous  stars  have  particular  names ;  the  most 
usual  mode  of  designation  being  the  use  of  the  letters  of  the  Greek 
alphabet,  alpha  (a)  being  given  to  the  brightest  star,  beta  (i3)  to  the 
next,  and  so  on.  When  the  twenty-four  letters  of  this  alphabet  are 
exhausted,  the  Roman  letters  are  used,  and  subsequently  the  Arabic 
numerals,  the  latter  being  applied  according  to  the  positions  of  the 
stars  in  the  constellation,  the  most  eastern  being  designated  1,  which 
is  thus  the  first  star  to  cross  the  meridian. 

ft.  The  Greek  Alphabet. — The  following  are  the  letters  of  the 
Greek  alphabet,  with  their  names.  It  will  be  convenient  for  the  student 
to  become  familiar  with  them,  as  they  are  very  frequently  employed. 


a     Alpha 

T]    Eta 

v    Nu 

T    Tau 

0    Beta 

0     Theta 

£     Xi 

v    Upsilon 

y     Gamma 

t      Iota 

o     Omicron 

</»    Phi 

(I     Delta 

K      Kappa 

7T      Pi 

X    Chi 

e     Epsilon 

/t     Lambda 

p     Rho 

V     Psi 

C     Zeta 

fj,    Mu 

a     Sigma 

w     Omega 

341.  The   constellations  are  distinguished  as  Northern, 
Zodiacal,  and  Southern,  according  to  their  positions  in  the 
heavens  with  respect  to  the  ecliptic.     The  zodiacal  constel- 
lations have  the  same  names  as  the  signs,  but  are  situated 
about  28°  to  the  east  of  them,  so  that  Aries,  although  the 
first  sign  of  the  ecliptic,  is  the  second  constellation  of  the 
zodiac  (Art.  105,  &). 

342.  The  WHOLE  NUMBER  of  constellations  is  109;  but 
many  of  them  are  not  generally  acknowledged  or  much 
used  by  astronomers  at  the  present  time. 

a.  The  following  catalogue  contains  the  names  of  the  principal  con- 
stellations, with  their  right  ascension  and  declination,  the  number  of 
stars  of  the  first  five  magnitudes  contained  in  each,  and  the  name  of 
the  astronomer  ly  whom  they  were  first  enumerated  or  invented : 

NOTE. — The  right  ascension  and  declination  of  the  central  points  of  the 
constellations  are  given. 

QUESTIONS.— ffl.  Use  of  letters?  Of  numerals?  Letters  of  the  Greek  alphabet? 
341.  How  are  the  constellations  divided?  343.  What  is  the  whole  number  of  constel- 
lations? Are  all  acknowledged  and  used?  a.  Which  are  the  principal  Northern 
constellations?  Zodiacal  constellations?  Name  the  Southern  counstellations. 


THE    STARS. 


233 


THE  NORTHERN  CONSTELLATIONS. 


1 

NAME. 

| 

MEANING. 

BY  WHOM 
ENUMERATED 
OE  INVENTED. 

a  c 

il 

R.A. 

DEO. 

1 

ANDROMEDA, 

The  Chained  Prince**, 

Ptolemy,  150 
A.D. 

18  |   15° 

85° 

2 

AQUILA, 

The  Eagle, 

Ptolemy. 

33    292-J0 

10° 

8 

AURIGA, 

The  Charioteer, 

Ptolemy. 

85  1  90" 

42° 

4 

BOOTES. 

The  Bear  Driver, 

Ptolemy. 

35  '219°  !.%" 

tf) 

CAM  ELOPARD  ALtTS, 

The  Giraffe, 

Hevelius,  1690. 

86 

66°  !C8° 

(i 

CANES  VENATICI, 

The  Hunting  Dog*, 

Hevelius,  1610. 

15 

195° 

40° 

7 

CASSIOPEIA. 

The  Queen  in  her  Chair 

Ptolemy. 

46 

mc 

CO" 

8 
8 

CEPHEUS, 
CLYPEUS  SOBIESKH, 

The  King, 
Sobienki's  Shield, 

Ptolemy. 
Hevelius,lC90. 

44 
4 

£2S° 
'272£° 

C6° 
15°  S 

10 

COMA  BERENICES, 

Berenice's  Hair, 

Tycho    Brahe, 
16(8. 

20 

190° 

25° 

11 

CORONA  BOEEALIS, 

The  Northern  Crown, 

Ptolemy. 

19 

285° 

80" 

12 

CYGNUS, 

The  Sican, 

PtoU-my. 

67 

8(5° 

42° 

1.'5 

DELPIIINUS, 

The  Dolphin, 

Ptolemy. 

10  1810° 

15° 

14 

DKACO, 

The  Dragon, 

Ptolemy. 

80 

'260° 

66° 

15 

EQUULEUS, 

The  Little  Horse,  or 
Hor«<Sv  Head. 

Ptolemy. 

5 

816° 

6° 

16 

HERCULES, 

Hercules, 

Ptolemy. 

f5 

251° 

27° 

17 

LACKUTA, 

The  Lizard, 

Hevelius,  1690. 

18 

805" 

44° 

18 

LKO  MINOR, 

The  Lesser  Lion, 

Hevelius,  1G90. 

16 

1M° 

36° 

19 

LYNX, 

The  Lynv, 

Hevelius,  1690. 

28 

120° 

506 

20 

LYRA, 

The  Harp, 

Ptolemy. 

18 

280° 

85° 

'21 

P  KG  A  SITS, 

The  Winged  Horse, 

Ptolemy. 

48 

886° 

16° 

22 

PERSEUS  ET  CAPUT  ME- 
DUSAE, 

Perseus  &  Medusa's 
Head, 

Ptolemy. 

40 

52r 

47° 

'2° 

SAO  ITT  A, 

The  Arrwe, 

Ptolemy. 

5 

295° 

18e 

24 

SERPKNS, 

The  Serpent, 

Ptolemy. 

28 

S86° 

10° 

25 

T  A  IT  KITS    PoNIATOWSKII, 

Poniatowfki'H  Bull, 

Poczobut,  1777 

6 

',67r 

5° 

2(5 

TllIANCrLl'M, 

The  Triangle, 

Ptolemy. 

5 

80° 

82° 

'27 

URSA  MAJOR, 

The  Great  Bear, 

Ptolemy. 

£3 

161*° 

fi8' 

28 

I'RSA  MINOR, 

The  7,<>S86r  -fiwrr, 

Ptolemy. 

28 

226" 

78* 

'29 

VULPECULA    KT    AN8KR. 

The  /Vw  ««</  Me  Goose, 

HeveliiiP,1690. 

28 

800° 

25° 

THE  ZODIACAL  CONSTELLATIONS. 


c 

NAME. 

MEANING. 

BY  WHOM 
ENUMERATED. 

l| 

R.  A. 

DEC. 

1 

ARIES, 

The  Ram, 

Ptolemy. 

17 

871" 

18°  N 

2 

TAURUS, 

The  Bull, 

Ptolemy. 

58 

65- 

18°" 

8 

GEMINI, 

The  Twins, 

Ptolemy. 

28 

105° 

25°  •• 

4 

CANCER, 

The  Crab, 

Ptolemy. 

15 

130" 

20°" 

B 

LEO, 

The  Lion, 

Ptolemy. 

47 

155° 

15°  " 

8 

VIRGO, 

The  Virgin, 

Ptolemy. 

89 

200° 

go  u 

7 

LIBRA, 

The  Balance, 

Ptolemy. 

28 

225° 

15°  S 

8 

SCORPIO, 

The  Scorpion, 

Ptolemy. 

84 

244° 

26°  "• 

9 

SAGITTARIUS. 

The  Archer, 

Ptolemy. 

88 

285" 

82°  " 

10 

11 

CAPRICORNUS, 
AQUARIUS, 

The  (zoflfc. 
The  Wfl<er-<7arr«er, 

Ptolemy. 
Ptolemy. 

22 
25 

315° 
880° 

•20°  " 

90  a 

121  PISCES, 

The  Fishes, 

Ptolemy. 

18 

6° 

10"  N 

234 


THE   STABS. 


THE  SOUTHERN  CONSTELLATIONS. 


c 

ft 

NAME. 

MEANING. 

BY  WHOM 
KNUMKKATKD 
OR  INVENTED. 

!i 

T 

K.  A. 

186° 

DBC. 

1    APIS  OB  MUSCA, 

The  Bee  or  Fly, 

Bayer,  1604. 

1  68° 

2 

ARA, 

The  Altar, 

Ptolemy. 

15 

256°  154° 

8 

AKQO, 

The  Ship  Argo, 

Ptolemy. 

18S 

115°    50" 

4 

CANIS  MAJOR, 

The  Great  Dog, 

Ptolemy.           j  27 

101° 

24° 

5 

CAMS  MINOR, 

The  Le**er  Dog, 

Ptolemy.           !     6 

111° 

5°N 

8 

CKXTAURUS, 

The  Centaur, 

Ptolemy. 

54 

195° 

48° 

7 

CKTUS, 

Tlie  W  hi  tie, 

Ptolemy. 

82 

80° 

12° 

8 

OOLUMBA   NOAOIII, 

Noah's  Dove, 

Hoy  cr,  1679. 

15 

81° 

35" 

9 

COROKA  AUSTKALIft, 

The  Southern  Crown, 

Ptolemy. 

7 

•277-r 

40° 

In 

CORVUS, 

The  Grow, 

Ptolemy. 

8 

185° 

18° 

11 

CRATER, 

The  Cup, 

Ptolemy. 

9 

170° 

15° 

12 

CRUX. 

The  Crow, 

Eoyer.  1679. 

10 

184° 

60° 

181  DORADO, 

14   ElUDANUB, 

The  S^c()rd•F^8h, 
The  tfifle/-  Po, 

Bayer,  1604. 
Ptolemy. 

17 
64 

7d° 
85° 

62° 
30° 

15  Gnus, 

The  Crane, 

Bayi-r,  1604. 

11 

385° 

4fe 

16 

HYDRA, 

The  Stti/Jfctf, 

Ptolemy, 

49 

ioi/° 

10* 

17 

Hvoiius, 

The  Water-  Snake, 

Bayer,  1604. 

'25 

40° 

70° 

IS 

INDUS, 

The  Indian, 

Buyer,  1604. 

15 

«5° 

55° 

19 

LEPUS, 

The  #ar«, 

Ptolemy. 

18 

81° 

20° 

'20 

LUPUS, 

;'he  HW/; 

Ptolemy. 

84 

231° 

45° 

'21 

MONOCEROS, 

'he  Unicorn, 

IIevelius,1690. 

12 

105° 

2° 

'22 

OPHIUOHUS  OR    SERPEN- 

TARIU8, 

The  Serpent  Carrier, 

ftolemy. 

40 

"55° 

0° 

23 

ORION, 

Tlie  Huntsman, 

Ptolemy. 

37 

82i° 

0° 

24 

PAVO, 

['he,  Peacock, 

Bayer,  1690. 

27 

290°  ;68° 

25 

PHOSNIX, 

fhe  Phoenix, 

Bayer,  1690. 

82 

15° 

5U° 

•2G 

PlSOI8  AUBTRALIS, 

The  Southern  Fifth, 

Ptolemy, 

16 

525° 

on* 

•27 

TOUCAN, 

The  American  (f  one, 

Baver,  1690. 

21 

556" 

66° 

88 

TRIANQDHTM  AUSTRALE, 

The  Southern   Triangle, 

Bayer,  1690. 

11 

J85"  !65° 

b.  History  of  the  Constellations. — The  following  is  a  brief 
account  of  the  origin  of  the  constellations : 

THE  NORTHERN  CONSTELLATIONS. 

Andromeda,  daughter  of  Cepheus,  king  of  Ethiopia,  who,  to  save 
his  kingdom,  caused  her  to  be  bound  to  a  rock  so  that  she  might  be 
devoured  by  a  sea  monster ;  but  she  was  rescued  by  Perseus,  who 
turned  the  monster  into  stone  by  presenting  to  it  the  head  of  Medusa, 
the  Gorgon  Queen,  whom  he  had  conquered  and  slain. 

Aquila,  according  to  the  ancient  fable,  was  king  of  one  of  the 
Cyclades,  but  was  changed  into  an  eagle  and  placed  among  the  stars. 
Tycho  Brahe  added  to  this  constellation  Antinous,  a  youth  of  Asia 
Minor,  greatly  celebrated  for  his  beauty,  who  lived  in  the  reign  of  the 
Emperor  Adrian. 


QxiE6TiON.— b.  What  is  the  history  of  each  ? 


THE    STARS.  235 

Auriga,  represented  as  a  man  kneeling,  and  holding  a  bridle  in  his 
riglit  hand,  and  a  goat  with  her  kids  in  his  left.  The  accounts  given 
of  this  constellation  arc  various  and  inconsistent.  Its  origin  is  un- 
known. 

Bootes,  represented  as  grasping  a  club  in  one  hand,  while  he  holds 
the  two  hunting  dogs  by  a  cord,  in  the  other.  He  seems  to  bo  driving 
the  two  bears  round  the  pole.  The  origin  of  this  constellation  is  lost 
in  antiquity. 

Canes  Venatici,  called  Asterion  and  Chara,  inserted  by  Hevelius, 
in  1G90.  They  are  held  in  a  leash  by  Bootes. 

Cassiopeia,  the  wife  of  Cepheus  and  mother  of  Andromeda. 

Cepheus,  king  of  Ethiopia,  supposed  to  have  gone  with  the  Argo, 
nauts  in  search  of  the  golden  fleece. 

Clypeus  or  Scutum  Sobieskii,  named  in  honor  of  John  Sobieski, 
King  of  Poland,  by  Hevelius,  who  flourished  during  his  reign. 

Coma  Berenices. — Berenice  was  the  Queen  of  Ptolemy  Euergetes, 
one  of  the  kings  of  Egypt ;  and  while  he  was  engaged  in  war,  she 
made  a  vow  to  dedicate  her  beautiful  hair  to  Venus  if  he  returned  in 
safety, — a  vow  which  she  fulfilled. 

Corona  Borealis,  a  beautiful  crown  said  to  have  been  given  by  the 
god  Bacchus  to  Ariadne,  a  Cretan  princess. 

Cygnus,  supposed  by  some  to  represent  the  famous  musician 
Orpheus,  who,  according  to  the  fable,  was  changed  into  a  swan,  and 
placed  near  his  lyre  in  the  heavens. 

Delphinus,  the  dolphin  who  is  caid,  in  the  fable,  to  have  persuaded 
Amphitrite  to  become  the  wife  of  Neptune,  though  she  had  made  a 
vow  of  perpetual  celibacy. 

Draco,  supposed  to  be  the  dragon  which  guarded  the  golden  apples 
in  the  garden  of  the  Hesperides,  near  Mount  Atlas,  and  was  slain  by 
Hercules. 

Equuleus  is  the  head  of  a  horse,  supposed  to  have  been  the  brother 
of  Pegasus,  and  given  to  Castor  by  Mercury. 

Hercules,  the  famous  Grecian  hero,  celebrated  for  his  many  won- 
derful exploits. 

Lyra,  the  harp  given  to  Orpheus  by  Apollo,  upon  which  he  played 
with  such  E.kill,  that  even  the  rivers,  it  is  fabled,  ceased  to  flow  in  order 
to  listen  to  his  strains. 

Pegasus,  the  winged  horse,  which,  according  to  the  Greek  fable, 
sprung  from  the  blood  of  Medusa,  after  Perseus  had  cut  off  her  head. 
Bellerophon,  attempting  to  fly  to  heaven  upon  his  back,  was  dashed  to 


236  THE   STARS. 

the  earth  ;  and  the  horse  continuing  his  flight  was  finally  placed  by 
Jupiter  among  the  constellations. 

Perseus,  son  of  Jupiter  and  Danae,  was  provided  with  celestial  arms, 
and  made  war  upon  the  three  Gorgons,  who  had  the  power  to  turn 
every  one  to  stone  on  whom  they  looked.  Medusa  was  the  most 
celebrated  for  her  beauty ;  but  her  hair  was  turned  to  serpents  by 
Minerva,  the  sanctity  of  whose  temple  she  had  violated.  (See  An- 
dromeda.) 

Sagitta,  the  arrow  of  Hercules  with  which  he  killed  the  vulture 
that  preyed  on  Prometheus,  who  was  tied  to  a  rock  on  Mount  Cauca- 
sus by  command  of  Jupiter. 

Serpens  and  Serpentarius,  or  Ophiuchus. — The  latter  is  supposed 
to  be  JEsculapius,  a  famous  Greek  physician.  He  holds  the  serpent  in 
his  hand  as  an  emblem  of  his  art,  the  cure  of  a  serpent's  bite  being  a 
test  of  medical  skill. 

Taurus  Poniatowskii,  a  small  constellation,  some  of  the  stars  of 
which  are  arranged  like  a  V,  fancied  to  resemble  a  bull's  head,  and 
named  as  above  after  Count  Poniatowski,  who  saved  the  life  of  Charles 
XII.  King  of  Sweden,  at  the  battle  of  Pultowa,  and  afterward  at  the 
battle  of  Ilugen. 

Triangulum. — This  constellation  represents  the  triangular  delta  of 
the  Nile. 

Ursa  Major,  suposed  to  represent  Calisto,  daughter  of  a  king  of 
Arcadia,  and  changed  into  a  bear  in  consequence  of  the  jealousy  of  Juno. 
Ursa  Minor  is  supposed  to  have  been  her  son  Areas,  changed  with  her. 
These  constellations  are  sometimes  called  Triunes ;  also,  the  Greater 
and  Lesser  Wains. 

THE  ZODIACAL  CONSTELLATIONS. 

These  are  supposed  to  have  been  invented  by  the  Egyptians  or 
Chaldeans  to  symbolize  the  changes  of  the  months  and  seasons.  The 
following  is  their  origin  according  to  the  Greeks : 

Aries  is  the  ram  that  bore  the  golden  fleece,  for  which  the  Argonauts 
undertook  their  expedition. 

Taurus  is  supposed  to  be  the  bull  whose  form  Jupiter  assumed  in 
order  to  carry  off  Europa,  a  beautiful  princess  of  Phoenicia.  She  was 
borne  across  the  sea  to  Europe,  and  gave  name  to  that  country.  This 
constellation  contains  five  stars  arranged  in  the  form  of  a  V,  and 
called  the  Hyades.  It  also  contains  the  Pleiades,  or  seven  stars,  as 


THE   STARS.  237 

the  number  is  declared  by  some  of  the  ancients,  although  only  six  are 
now  visible. 

Gemini,  the  twin  brothers  Castor  and  Pollux,  sons  of  Jupiter  and 
Leda,  a  Spartan  queen.  They  were  celebrated  for  their  valor  and 
heroic  deeds,  and  were  afterward  worshiped  as  deities. 

Cancer,  the  sea-crab,  sent  by  Juno  to  annoy  Hercules.  This  con- 
stellation more  probably  symbolizes  tfie  backward  movement  of  the 
sun  when  at  the  northern  solstice. 

Leo,  the  famous  Nemean  lion,  slain  by  Hercules  ;  or  a  symbol  of 
the  intense  heat  of  the  season  when  this  asterism  is  on  the  meridian. 

Virgo,  the  Virgin  Astrsea,  goddess  of  justice,  who  lived  on  earth 
during  the  golden  age,  but  returned  to  heaven  and  was  placed  among 
the  stars.  A  symbol,  probably,  of  the  time  of  harvest,  as  she  holds  an 
ear  of  corn  (spica  mrginw)  in  her  hand. 

Libra,  the  scales  which  Virgo,  the  goddess  of  justice,  used  as  an 
emblem  of  her  office.  Most  probably  it  was  an  emblem  of  the  bal- 
ance or  equality  of  the  days  and  nights. 

Scorpio,  a  very  ancient  constellation,  supposed  to  typify  the  deadly 
influences  of  the  season  when  the  sun  is  in  this  part  of  the  ecliptic. 
According  to  Ovid,  it  is  the  scorpion  which  stung  Orion  and  caused  his 
death. 

Sagittarius,  emblem  of  the  hunters'  season,  inscribed  on  the  Egyp- 
tian Zodiac.  According  to  the  Greeks,  it  represents  Chiron,  the 
famous  Centaur,  who  changed  himself  partly  into  a  horse. 

Capricornus,  emblem  of  the  sun's  climbing  (as  a  goat)  from  the 
winter  solstice.  In  the  Greek  fables,  it  is  the  goat  into  which  Bacchus 
changed  himself  to  escape  the  giant  monster  Typhon. 

Aquarius,  emblem  of  the  wet  season.  The  Greeks  took  it  for 
Ganymede,  the  cup-bearer  of  Jupiter. 

Pisces,  emblem  of  the  fishing  season.  The  Greeks  represent  them 
to  be  the  fishes  into  which  Venus  and  Cupid  changed  themselves  to 
escape  the  giant  Typhon. 

THE  SOUTHERN  CONSTELLATIONS. 

Ara,  the  altar  on  which,  according  to  the  ancient  mythology,  the 
gods  swore  before  their  celebrated  contest  with  the  giants. 

Argo,  the  ship  in  which  the  Argonauts  sailed  in  quest  of  the  golden 
fleece. 

Canis  Major  and  Canis  Minor,  supposed  to  be  Orion's  hounds. 


238  THE   STARS. 

Centaurus,  one  of  the  Centaurs,  a  fabulous  race,  half  men  and  half 
horses ;  most  probably  a  tribe  of  men  who  invented,  or  were  skilled 
in,  the  art  of  breaking  in  horses. 

Cetus,  the  sea  monster  from  which  Andromeda  was  rescued  by 
Perseus. 

Corvus,  the  crow  sent  by  Apollo  to  watch  the  conduct  of  his  mis- 
tress Coronis,  and  rewarded  by  being  placed  in  the  heavens. 

Crater. — The  origin  of  this  constellation  appears  to  be  unknown. 

Crux,  formed  by  Royer  as  a  Christian  emblem.  It  contains  four 
stars  that  form  a  cross,  two  of  them  pointing  directly  to  the  south  pole. 

Eridanus,  the  river  Po,  fabled  to  have  received  Phaeton,  who,  having 
undertaken  to  guide  the  chariot  of  the  sun,  was  struck  by  Jupiter  with 
a  thunderbolt,  to  prevent  the  general  conflagration  of  the  world  from 
the  ignorance  of  the  rash  youth. 

Hydra,  a  monstrous  serpent  killed  by  Hercules.  It  is  supposed  by 
some  to  symbolize  the  moon's  course. 

Lepus,  placed  near  Orion,  as  being  one  of  the  animals  hunted  by 
him. 

Lupus,  a  king  of  Arcadia,  Lycaon,  changed  into  a  wolf  on  account 
of  his  cruelties. 

Ophiuchus. — See  Serpens. 

Orion,  according  to  the  Greeks,  a  famous  hunter,  who,  as  a  punish- 
ment for  his  profane  boasting,  was  bitten  by  the  scorpion  and  killed. 
This  constellation  is  mentioned  in  the  bock  of  Job,  and  is  therefore  of 
very  great  antiquity.  Some  think  that  it  represents  Nimrod,  "  the 
mighty  hunter/'  mentioned  in  Genesis. 

Piscis  Australis,  supposed  by  the  Greeks  to  be  Venus,  transformed 
into  a  fish  to  escape  the  giant  Typhon. 

c.  Of  the  48  constellations  enumerated   by  Ptolemy  in  his  great 
work,  the  Almagest,  all  except  three  are  described  in  a  poem  styled 
Phenomena,  written  in  Greek  by  Aratus,  a  Cilician  poet,  270  B.C., 
and  still  extant.      This  poem  is,  however,  only  a  paraphrase  of  a 
celebrated  work  written  about  370  B.C.  by  Eudoxus,  a  contemporary 
of  Plato,  and  containing  an  account  of  all  the  constellations  used  hi 
his  time. 

d.  The  following  synopsis  shows  the  relative  positions  as  to  right 

QUESTIONS. — d.  Names  of  the  constellations  in  the  circle  of  perpetual  apparition,  from 
west  to  east?  Between  50°and  25°  of  north  declination?  Between  25°  and  0°  ?  Be- 
ween  0°  and  25°  S  ?  Between  25°  and  50°  S? 


THE   STARS. 


239 


ascension  and  declination  of  the  constellations  visible  in  this  latitude. 
If  studied  in  this  order  they  will  be  found  without  difficulty  on  the 
globe  or  in  the  heavens. 
NOTE. — Each  line  in  this  table  represents  about  30°  of  right  ascension. 

TABLE    SHOWING    THE    POSITIONS    OF    THE    CONSTELLA- 
TIONS IN  THE  HEAVENS. 


NORTH    DECLINATION. 


SOUTH    DECLINATION. 


90°—  50° 

50°—  25° 

25°—  0° 

ZODIAC. 

0°—  25° 

25°—  50° 

Cassiopeia 

Andromeda 

Places 

Cetus 

Triansulum 

Aries 

Phoenix 

Cameloparcl. 

Perseus 

Taurus          -J 

Lepns             j 
Orion              \ 

K.idanus 
ColumLa 

Auriga 

Can  is  Minor 

Gemini         -j 

Can  is  Major 
Monoceros 

Argo 

Lynx 

Cancer 

Ursa  Major 

Leo  Minor 

Leo 

Hydra 

Crater 

Canes  Ven. 

Coma  Ber. 

Virgo 

Cor  v  us 

Centatirus 

Ursa  Minor  -J 

Bootes 
Corona  Bor. 

Serpens 

Libra 

Lupus 

Draco 

Hercules 

Taurus  Pon. 

Scorpio 

Ophiuclnis 

Lyra 

Sayitta 
Aquila 

Sagittarius 

Clyp.  Sobiesk. 

Corona  Ans 

Cepheus         4 

Laccrta 
Cygnus 

Oelplnnns 
Equuleus 

Capricornus 

Pegasus 

Aquarius 

Grus 

e.  Each  column  of  this  table  contains  the  constellations  as  they 
are  arranged  from  west  to  east ;  and  each  line  read  from  left  to  right, 
gives  the  constellations,  from  north  to  south,  that  are  on  or  near  the 
meridian  at  the  same  time.  By  knowing  the  time  that  each  zodiacal 
constellation  comes  to  the  meridian,  remembering  that  these  constel- 
lations are  about  30°  east  of  the  signs,  and  that  those  are  on  the 
meridian  at  midnight  which  are  opposite  to  the  sun's  place  at  noon, 
the  student  with  a  little  consideration  will  be  able  to  find  the  position  of 
the  constellations  at  any  hour  and  on  any  evening  during  the  year. 
The  position  at  any  time  of  the  evening  can  easily  be  deduced  from 
that  at  midnight  by  reckoning  for  each  hour  15°,  toward  the  east  if 
the  time  is  earlier,  and  toward  the  west,  if  later. 


QUESTION. — Use  of  (he  table? 


240 


THE    STARS. 


343.  STAB  NAMES. — Only  a  very  few  of  the  stars  are  dis- 
tinguished by  particular  names,  the  usual  mode  of  designation 
being  by  means  of  letters  or  numbers. 

The  following  is  a  list  of  the  most  noted  or  conspicuous  of  the  stars 
with  their  special  names,  literal  designations,  magnitudes,  and  situations : 

NOTE.— In  the  literal  designations,  the  letter  is  followed  by  the  Latin 
name  of  the  constellation,  in  the  possessive  case;  thus,  a  Centauri  means 
the  brightest  star  of  Centaurus ;  ft  Tauri,  the  second  star  of  Taurus  ;  y  Cas- 
siopeia, the  third  star  of  Cassiopeia,  etc.  The  stars  are  arranged  in  this 
list  according  to  their  magnitudes. 

LIST  OF  PRINCIPAL  STARS. 


NAME. 

LITERAL  DESIGNATION. 

SITUATION. 

z 

< 

33 

< 

pa 

DEC. 

SlRlUS 

a  Cani*  Miijoris 

Nose  of  the  Great  Dog 

100° 

1<H"  S 

CANOPUS 
ARCTURUS 

a.  Argil  n 
a  Bootix 

The  Ship  Argo 
Knee  of  Bootes 

95° 

212° 

52i°  S 
'20°  N 

BETELGEUSE 

a.  Orioni* 

Shoulder  of  Orion 

87" 

7$'N 

RlGEL 

ft  Orionis 

foot  of  Orion 

77* 

8*'   8 

C  A  PELL  A 

a  Atirigce 

Gout  of  Auriga 

77° 

4ti°N 

VKOA 

a  Lyres, 

One  of  the  strings  of  the  Harp 

278° 

39°  N 

PROCYON 

a  C<tnix  Minoris 

The  Little  Dog 

113° 

5i°  N 

ACHKRNAR 

a.  Erid(tni 

The  River  Po 

23° 

58°  S 

ALDEBARAN 

x  Tdiiri 

Eye  of  the  Bull 

'     67° 

16|°N 

A  NT  ARKS 

>  S-orpionis 

Heart  of  the  Scorpion 

245° 

26°  S 

ALT  \  IB 

SPICA 

FoMALHAtTT 

j.  Aqniloe, 
x   Virgini* 

a  Pimrix  AtUfi. 

Neck  of  the  Eagle 
Sheaf  of  Virgo 
Southern  Fish 

300'    8i°  N 
200'  10i*  S 
343°  805°  S 

RKOULUS               01  Leoni* 

Heart  of  the  Lion 

150°  12r  N 

DEXRH                   *  dugnl 

Tail  of  the  Swan 

309"!  45'  N 

ALPIIKRATZ           a.  Andromeflce, 

Head  of  Andromeda 

r|2sr  N 

DUHIIR                  !*  UfMce  M  ijori* 

Great  Bear 

i    1C4° 

oar  N 

CASTOR 
POLLUX 

a  Geminorum              \ 
3  ffsminorum             j 

Heads  of  Gemini 

' 

112° 
114° 

32°  N 
2S>-°  N 

POLE-STAR 

a  U>'*(K  Minor-is 

Tail  of  Little  Bear 

•2 

18i* 

882*  N 

ALPHARD 

i  f/i/'/rcK 

Heart  of  Hydra 

•J 

140° 

S°  S 

HAS  ALHAGUS 

a  Ophiucki 

Head  of  Serpent-bearer 

•> 

262° 

i2r  N 

MAKKAB 

a  Peyaxi 

Wing  of  Pegasus 

2 

845° 

145°  N 

ScilKAT 

ft  Pe'gaxi 

Thigh  of  Pegasus 

2 

345° 

27i°N 

ALGENIB 

y  Pefftifti 

Wins  of  Pegasus 

2 

2° 

u|°  N 

ALGOL 

ft  Perxei 

Head  of  Medusa 

2i      45°  401°  N 

DKNEBOLA 

ft  Leonix 

Tail  of  the  Lion 

2|i  176°    15°  N 

ALPIIKOCA 

a.  Coronce  Bar. 

Northern  Crown 

2i 

282° 

27°  N 

BENKTNASCH 
ALDKKAMIN 

VlNDEMIATRtX 

TJ   U  -see  Major  is 
a  Cep/iei 
e    Virginia 

Tip  of  the  Great  Bear's  Tail 
Breast  of  Cepheus 
Right  Arm  of  Virsro 

I3 

8 

206° 
318° 
194° 

50°  N 
62°  N 
1H°  N 

COR  CAROLI 

a  Cnn-um  Venaticorum 

The  Hunting  Docs 

8 

398  • 

39°  N 

ALCYONE 

i\  Tauri 

The  Pleiades 

8 

55° 

28fN 

QUESTIONS.—  343.  To  what  extent  are  star-names  used?    Mention  some  of  the  prin- 
cipal. 


THE    STARS.  241 

PROBLEMS  FOR  THE  CELESTIAL  GLOBE. 

PROBLEM  I. — To  find  the  place  of  a  constellation  or  star  on 
the  globe :  Bring  the  degree  of  right  ascension  belonging  to 
the  constellation  or  star  to  the  meridian ;  and  under  the 
proper  degree  of  declination  will  be  the  constellation  or 
star,  the  place  of  which  is  required. 

NOTE. — The  student  should  be  exercised  in  finding  the  places  of  all  the 
constellations  or  stars  laid  down  in  the  lists,  according  to  this  rule.  The 
place  of  a  planet  or  comet  may  also  be  found  by  this  rule  when  its  right 
ascension  and  declination  are  given. 

PROBLEM  II. — To  find  the  appearance  of  the  heavens  at  any 
place,  the  hour  of  the  day  and  the  day  of  the  month  being  given : 
Make  the  elevation  of  the  pole  equal  to  the  latitude  of  the 
place ;  find  the  sun's  place  in  the  ecliptic,  bring  it  to  the 
meridian,  and  set  the  index  to  12.  If  the  time  be  before 
noon,  turn  the  globe  eastward;  if  after  noon,  turn  it  west- 
ward till  the  index  has  passed  over  as  many  hours  as  the 
time  wants  of  noon,  or  is  past  noon.  The  surface  of  the  globe 
above  the  wooden  horizon  will  then  show  the  appearance  of 
the  heavens  for  the  time. 

NOTE. — The  student  must  conceive  himself  situated  at  the  centre  of  the 
globe  looking  out. 

PROBLEM  III. — To  find  the  declination  and  right  ascen- 
sion of  any  constellation  or  star :  Proceed  in  the  same 
manner  as  to  find  the  latitude  and  longitude  of  a  place  on 
the  terrestrial  globe. 

STAR    FIGURES 

344.  Particular  stars  can  be  easily  recognized  in  the  heav- 
ens by  noticing  the  configurations  which  they  form  with 
each  other,  or  by  using  the  more  conspicuous  stars  as 
"  pointers ;"  that  is,  by  assuming  two  bright  stars  so  situated 

QTTESTION, — 344.  How  to  find  particular  stars  ? 


242  THE    STAES. 

that  a  straight  line  drawn  through  both  will  point  directly 
to  the  less  prominent  star  whose  position  it  is  desired  to 
ascertain. 

«.  This  is  sometimes  called  the  method  of  "  alignments,"  and  is 
that  usually  employed  by  astronomers.  A  few  examples  are  here 
given  in  order  to  enable  the  student  to  find  some  of  the  most  conspic- 
uous of  the  stars. 

1.  The  Great  Dipper,  or  Charles's  Wain.— This  consists  of  seven 
bright  stars,  in  the  Great  Bear,  so  situated  as  to  resemble  a  dipper 
with  a  bent  or  curved  handle,  four  of  the  stars  forming  the  bowl,  and 
three,  the  handle.     It  is  situated  within  the  circle  of  perpetual  appari- 
tion, and  hence  is  always  visible,  although  in  different  positions  as  it 
revolves  around  the  pole.     The  two  stars  at  the  far  side  of  the  bowl 
(a  and  0)  are  called  the  "  pointers"  because  a  line  drawn  through  them 
would  reach  the"  pote-star,  which  can,  therefore,  always  be  found  by 
discovering-  the  Great  Dipper.     The  pole-star,  by  modern  astronomers 
called  Polaris,  by  the1  Greeks  Cynosura,  and  by  the  Arabians  Alrucca- 
lah,  is  situated  abolit  1£°  from  the  pole,  and  forms  the  extremity  of 
the  upwardly  curved  handle  of  a  small  dipper,  which  occupies  a 
reversed  position  froni  that  of  the  Great  Dipper,  and  consists  of  quite 
faint  stars. 

2.  Trapezium  of  Draco. — About  90°  east  of  the  Great  Dipper  are 
four  stars  so  arranged  as  to  form  an  irregular  quadrangle  or  trapezium. 
These  are  in  the  head  of  Draco,  and  with  another,  a  little  to  the  west, 
situated  in  the  nose  (Rastaberi),  form  almost  the  letter  V,  pointing  to 
the  west. 

3.  The  Chair  of  Cassiopeia. — This  consists  of  five  stars  of  the  3d 
magnitude,  which,  with  one  or  two  smaller  ones,  form  the  figure  of  an 
inverted  Chair ;  it  is  situated  almost  precisely  at  the  opposite  side  of  the 
pole  from  the  Dipper,  being  nearly  180°  from  it  and  in  about  the  same 
declination ;  it  can  thus  be  easily  found. 

4.  The  Great  Square  of  Pegasus.— South  of  the  Chair  and  a  little  to 
the  west,  are  four  stars  about  15°  apart,  forming  a  large  square.    They 
are  quite  bright  stars  and  the  figure  is  very  obvious.   The  north-eastern 
star  is  Alpheratz,  in  the  head  of  Andromeda ;  the  south-eastern,  Alge- 
nib ;    the    south-western,   Markab ;    and  the  north-western,   Scheat. 
Algenib  and  Alpheratz  are  on  the  equinoctial  colure,  which  being  con- 
tinued toward  the  north  passes  through  Caph,  in  Cassiopeia. 

QUESTIONS.—  ft.  "What star-figures  are  described?    What  is  the  situation  of  each? 


THE    STA11S.  243 

5.  The  Great  Y  of  Bootes. — This  consists  of  the  bright  and  pecu- 
liarly ruddy  star  Arcturus,   at  the  lower  extremity  of  the  letter; 
Mirach,  at  the  fork ;  Seginus,  at  the  extremity  of  the  western  arm ; 
and  Alphecca,  in  Corona  Borealis,  at  that  of  the  eastern.     This  figure 
is  less  than  45'  to  the  south-east  of  the  Great  Dipper.    Arcturus  and 
Seginus  form  with  Cor  Caroli,  situated  toward  the  west,  a  large  triangle  ; 
and  a  similar  but  a  larger  figure  is  also  formed  by  Arcturus  with  Dene- 
bola,  about  35°  west,  and  Spica  Virginia,  about  as  far  south. 

6.  The  Diamond  of  Virgo  is  a  large  and  very  striking  figure  formed 
of  Cor  Caroli  and  Spica  Virginis,  at  the  extremities  of  its  longest 
diagonal,  and  Arcturus  and  Denebola  at  those  of  the  shortest.     The 
former  are  about  50°  apart ;  the  hitter  35j°.     The  figure  extends  from 
north  to  south. 

7.  The  Cross  of  Cygnus. — This  consists  of  five  stars  so  arranged 
as  to  form  a  large  and  regular  cross,  the  one  at  the  upper  extremity 
being  Deneb,  a  star  of  the  first  magnitude.     This  figure  is  very  mani- 
fest and  is  situated  about  35°  to  the  west  of  the  Square  of  Pegasus. 
The  star  at  the  lower  extremity  of  the  cross  is  called  Albirco.    Deneb, 
or  Deneb  Cygni  (Deneb  means  tail),  is  sometimes  called  Arided.    A 
short  distance  toward  the  west  from  the  Cross  is  the  bright  star  Vega, 
forming  with  two  faint  stars  near  it  a  small  triangle,  the  base  being 
turned  toward  the  side  of  the  cross. 

8.  The  Sickle  of  Leo.— If  the  line  joining  the  "  pointers  "  of  the 
Great  Dipper  be  continued  toward  the  south,  it  will  pass  through  a  most 
beautiful  object,  having  the  complete  form  of  a  sickle,  the  bright  star 
Regulux  being  at  the  extremity  of  the  handle,  and  the  curve  of  the 
blade  toward  the  north-east. 

9.  The  V  of  Taurus. — This  is  a  group  of  stars  situated  in  the  head 
of  the  Bull,  the  brightest  of  which  is  Aldebaran,  a  ruddy  star  of  the 
first  magnitude,  and  situated  at  the  left  upper  extremity  of  the  letter. 
Aldebaran  is  an  Arabic  word  and  means,  "  that  which  follows :"  it  was 
applied  to  this  star  because  it  follows  the  Pleiades.    This  group  of 
stars  is  called  the  Hyades.    A  little  to  the  north-west  is  the  famous 
cluster  of  small  stars  called  the  Pleiades,  said  once  to  consist  of  seven 
stars,  although  now  we  only  discover  six,  of  which  Alcyone  is  the 
brightest, 

10.  The  "  Bands  of  Orion." — These  are  in  a  splendid  group  of 
stars  to  the  south-east  of  Taurus,  and  situated  under  the  equinoctial, 
consisting  of  four  brilliant  stars  in  the  form  of  a  long  quadrangle 


244  THE    STARS. 

intersected  in  the  middle  by  three  stars  arranged  at  equal  distances  in 
a  straight  line,  and  pointing  to  Sirius,  the  most  splendid  star  in  the 
heavens,  on  one  side,  and  the  Hyades  and  Pleiades  on  the  other.  These 
three  stars  have  been  called  by  some  "  The  Yard  ; "  in  the  Book  of  Job 
they  are  called  the  Bands  of  Orion.  A  line  of  faint  stars  projects  from 
these  toward  the  south :  these  are  sometimes  called  "  The  Ell."  At  the 
north-east  extremity  of  the  quadrangle  is  Betefgeuse ;  at  the  south-east, 
Saiph  ;  at  the  south-west,  Rigel ;  and  at  the  north-west,  Bellatrix. 

tl.  The  Crescent  of  Crater. — To  the  south-east  of  the  Sickle  may 
be  distinctly  seen  a  beautiful  crescent  or  semi-circle  opening  toward 
the  west,  consisting  of  stars  of  the  sixth  magnitude.  They  form  the 
outlines  of  Crater ;  and  nearly  south  of  the  Sickle  is  the  bright  star 
Cor  Hydras,  almost  solitary  in  the  heavens. 

12.  The  Dipper  of  Sagittarius. — This  is  a  very  striking  figure  con- 
sisting of  five  stars  of  the  3d  and  4th  magnitudes,  forming  a  straight- 
handled  dipper  turned  bottom  upward.  It  is  a  considerable  distance 
south  of  Lyra,  but  comes  to  the  meridian  a  very  short  time  after  it. 
The  stars  at  the  mouth  of  the  dipper  are  about  5°  apart. 

Familiarized  with  these  few  configurations,  it  will  not  be  difficult 
for  the  student,  with  the  assistance  of  the  globe  or  a  planisphere,  to 
acquire  a  knowledge  of  the  other  visible  stars  and  their  positions  in 
the  constellations  to  which  they  belong. 

345.  The  APPARENT  PLACES  of  the  stars  are  constantly 
changing  in  consequence  of  the  precession  of  the  equinoxes. 
Their  right  ascensions  and  declinations  are  either  increasing 
or  diminishing,  according  to  their  situation,  as  the  equinoctial 
pole  revolves  around  that  of  the  ecliptic. 

a.  The  star  Polaris  is  about  H°  from  the  pole,  and  is  making  a 
constant  approach  to  it ;  which  it  will  continue  to  do  until  its  dis- 
tance is  about  \°.  It  will  then  recede  till  in  about  12,000  years  the 
bright  star  Vega,  which  is  now  51°  20'  from  the  pole  will  be  less  than 
5°  from  it,  and  will  therefore  be  the  pole-star.  About  4,000  years  ago 
a  Draconis  was  the  polar  star,  being  about  10'  from  the  pole. 

346.  NUTATION. — The  precession  of  the  equinoxes  is  not 
a  uniform  movement,  hut  is  subject  to  periodical  variations 

QUESTIONS.— 345.  Are  the  stars  absolutely  "  fixed  r  What  change  constantly  occurs! 
« .  What  change  in  the  pole-star  ?  346.  What  is  nutation  ?  How  caused  ? 


THE    STARS.  245 

occasioned  by  the  different  positions  of  the  sun  and  moon 
with  respect  to  the  plane  of  the  equinoctial.  When  the  sun 
is  at  the  equinox  its  effect  is  nothing;  at  the  solstice  it  is 
at  its  maximum ;  and  thus  arises,  in  connection  with  the 
general  revolution  of  the  pole,  a  vibratory  motion  of  the 
earth's  axis,  called  nutation.* 

347.  The  SOLAR  NUTATION  is  very  slight  and  goes  through 
all  its  changes  in  one  year ;  but  that  of  the  moon,  depend- 
ing on  the  position  of  its  nodes  with  respect  to  the  earth's 
equinoxes,  requires  a  period  of  18^  years.     The  latter  is  what 
is  ordinarily  meant  by  nutation. 

a.  By  the  lunar  nutation  alone,  the  pole  of  the  equator  would  be 
made  to  describe,  in  18^  years,  a  small  ellipse,  about  18^"  by  13J",  the 
longer  axis  being  in  the  direction  of  the  ecliptic  pole  ;  but  being  car- 
ried by  the  general  movement  of  precession  round  the  pole  of  the 
ecliptic  at  the  rate  of  50"  annually,  it  actually  moves  in  a  circle  the 
circumference  of  which  is  an  undulating  curve,  somewhat  like  the  real 
orbit  of  the  moon,  the  limit  of  the  undulation  either  way  being  9V'. 

6.  The  discovery  of  the  nutation  of  the  earth's  axis  was  made  by 
Dr.  James  Bradley  in  1727,  by  noticing  slight  variations  in  the  right 
ascensions  and  declinations  of  the  stars  of  which  neither  precession 
nor  any  other  known  source  of  disturbance  would  account.  The  true 
cause  of  the  phenomena  soon  suggested  itself  to  his  mind,  but  could 
not  be  confirmed  until  after  18^  years  of  observation.  It  was  there- 
fore not  announced  till  1745. 

348.  ABERRATION. — This   is  a  change  in  the  apparent 
places  of  the  stars,  which  arises  from  the  motion  of  the 
earth  in  its  orbit,  combined  with  the  progressive  motion  of 
light. 

(i.  This  displacemqnt  qf  the;  stars  was  first  observed  by  Hooke 
while  attempting  to  discover  a  parallax  in  y  Draconis  •  but  the  true 
explanation  of  its  cause  was  given  by  Dr.  Bradley  in  1727, — the  year 

^Nutation  is  derived  from  a  Latin  word  wjiich  means  a  nodding. 

QUESTIONS.—  347.  Periods  of  the  solar  and  lunar  nutations?  «,  Effect  of  the  lunar 
nutation  ?  b.  By  whoiu  and  how  discorered  ?  84$,  What  is  aberration  ?  «.  Ho\r 
and  when  discoyered  f 


246  THE    STABS. 

in  which  the  death  of  Ne  vton  took  place.  It  was  one  of  the  most 
interesting  and  important  astronomical  discoveries  ever  made,  and 
afforded  an  entire  confirmation  of  the  progressive  motion  of  light,  dis- 
covered by  Roemer  about  50  years  previously. 

b.  Cause  of  Aberration. — An  object  is  always  seen  in  the  direction 
in  which  the  rays  of  light  coming  from  it  strike  the  eye.     Now  this 
depends  not  only  on  the  actual  direction  of  the  rays  themselves,  but 
on  our  own  motion  with  reference  to  them  ;  for  if  a  ray  is  proceeding 
perpendicularly  from  an  object  and  we  are  moving  directly  across  it,  it 
will  appear  to  strike  against  the  eye  in  an  oblique  direction,  and  thus 
the  object  will,  in  appearance,  be  thrown  forward  of  its  true  place,  by 
an  angle  depending  for  its  size  upon  the  ratio  of  the  velocity  of  our 
own  motion  to  that  of  light.     This  change  of  direction  of  the  rays  of 
light  is  similar  to  that  which  takes  place  in  the  drops  of  rain  when 
we  are  running  in  a  shower,  and  the  rain  descends  perpendicularly  ;  for 
then  it  beats  in  our  faces  as  it  would  if  we  were  standing  still  and  the 
wind  were  blowing  it  obliquely  against  us. 

c.  Amount  of  Aberration. — Since  the  velocity  of  light  is  184,000 
miles  a  second  while  that  of  the  earth  is  but  little  more  than  18  miles. 
the  ratio  of  the  latter  to  the  former  is  about  .0001,  which  is  the  sine  of 
an  angle  of  20^'  ;    and  this  accordingly  is  the  amount  of  displacement 
due  to  aberration,  when  the  star  is  so  situated  that  the  rays  proceed- 
ing from  it  are  perpendicular  to  the  plane  of  the  earth's  orbit,   the 
star  in  that  case  appearing  each  year  to  describe  a  small  circle  having 
a  radius  of  20.^".    When  the  rays  are  oblique  to  this  plane,  the  circle  is 
foreshortened  into  an  ellipse,  and  the  amount  of  displacement  varies, 
being  20^"  only  when  the  rays  are  perpendicular  to  the  earth's  motion  ; 
while  in  the  case  of  stars  situated  in  the  plane  of  the  ecliptic,  there  ia 
merely  an  apparent  oscillation,  in  a  straight  line,  amounting  to  41" 
during  each  revolution  of  the  earth. 

(I.  The  phenomena  connected  with  aberration  are  thus  very  compli- 
cated ;  and  as  they  are  all  satisfactorily  explained  by  the  hypotheses  of 
the  earth's  motion  and  that  of  light,  both  receive  a  confirmation  from 
this  important  discovery. 

349.  THE  GALAXY,  OK  MILKY  WAY  is  that  faint  lumi- 
nous zone  which  encompasses  the  heavens,  and  which,  when 

QUESTIONS. — b.  Its  cause  ?  c.  Amount  of  displacement  caused  by  it  ?  <7.  What  is 
proved  by  it  ?  349.  What  is  the  Galaxy  or  Milky  Way  ? 


THE    STARS.  24? 

examined  with  a  telescope,  is  found  to  consist  of  myriads  cf 
stars.  Its  general  course  is  inclined  to  the  equinoctial  at  an 
angle  of  63°,  and  intersects  it  at  about  105°  and  285°  cf 
•right  ascension.  Its  inclination  to  the  plane  of  the  ecliptic 
is  consequently  about  40°. 

a.  This  nebulous  zone  is  of  very  unequal  breadth,  not  exceeding  in 
some  parts  3°  ;  while  in  others  it  is  10°  or  even  16°  ;  the  average 
breadth  being  about  10°.  It  passes  through  Cassiopeia,  Perseus, 
Gemini,  Orion,  Monoceros,  Argo,  the  Southern  Cross,  Centaurus,  Ophiu- 
chus,  Serpens,  Aquila,  Sagitta,  Cygnus,  and  Cepheus.  From  a  Centauri 
to  Cygnus  it  is  divided  into  two  parts,  the  whole  breadth  including  the 
two  branches  being  about  22°.  It  exhibits  other  divisions  at  several 
points  of  its  course. 

350.  Its   appearance  is    not  uniform,  some   parts  being 
exceedingly  brilliant ;  while  others  present  the  appearance  of 
dark  patches,  or  regions  comparatively  destitute  of  stars. 

a.  Near  the  Southern  Cross,  where  its  general  appearance  is  most 
brilliant,  there  occurs  a  singular  dark,  pear-shaped  space,  obvious  to 
the  most  careless  observer.     To  this  remarkable  patch  the  early  navi- 
gators gave  the  name  of  the  coal-sack.     A  similar  vacant  space  occurs  in 
the  northern  hemisphere  at  Cygnus. 

b.  The  number   of  stars   in   the    Milky  Way  is   inconceivably 
great.     Sir  William  Herschel  states  that  on  one  occasion  he  calculated 
that  116,000  stars  passed  through  the  field  of  his  telescope  in  a  quarter 
of  an  hour,  and  on  another  that  as  many  as  258,000  stars  were  seen  to 
pass  in  41  minutes.     The  total  number,  therefore,  can  only  be  esti- 
mated in  millions.     Struve's  estimate  of  the  whole  number  visible  in 
Sir  William  Herschel's  great  reflecting  telescope  is  20^  millions  ;  and 
tlie  number  brought  into  view  by  the  still  more  powerful  instrument 
cf  Lord  Rosse  must  be  very  much  greater. 

351.  The  PREVAILING  THEORY  with  regard  to  the  Milky 
Way  is,  that  it  is  an  immense  cluster  of  stars  having  the  gen- 
eral form  of  a  mill-stone,  split  at  one  side  into  two  folds,  cr 

QUESTIONS.— Its  position  ?  a.  Its  breadth?  What  constellations  does  it  pass  through  ? 
851.  Appearanco  of  the  Mi'ky  Way  ?  a.  The  "  coal-sack  ?"  b.  Number  of  stars  in 
the  Galaxy?  351.  What  is  it  supposed  to  be  ?  Its  figure  ? 


248  THE    STARS. 

thicknesses,  inclined  at  a  small  angle  to  each  other ;  that  all 
the  stars  visible  to  us  belong  to  this  system ;  and  that  the 
sun  is  a  member  of  it  and  is  situated  not  far  from  the  mid- 
dle of  its  thickness,  and  near  the  point  of  its  separation. 

(i.  The  fact  that  the  Milky  Way  is  composed  of  vast  numbers  of 
stars  was  conjectured  by  Pythagoras  and  other  ancient  astronomers, 
but  was  not  positively  discovered  till  Galileo  directed  his  telescore 
to  the  heavens.  The  hypothesis  that  it  is  a  vast  cluster  of  which  tie 
sun  and  visible  stars  are  members,  was  first  suggested  by  Th<  mas 
Wright  in  a  work  entitled  the  "  Theory  of  the  Universe,"  published 
in  1750.  This  subject  received  a  careful  and  prolonged  investigation 
by  Sir  William  Herschel,  the  results  of  which  he  published  in  1184, 
and  which  seems  to  establish  the  hypothesis  mentioned  in  the  text. 
This  opinion  he  arrived  at  by  taking  observations  at  different  distances 
from  the  zone  of  the  Galaxy,  and  counting  the  stars  within  the  field  of 
view.  On  the  supposition  that  the  stars  are  uniformly  distributed 
throughout  the  system,  the  number  thus  presented  would  indicate  the 
extent  of  the  cluster  in  the  direction  in  which  they  were  seen  ;  and  in 
this  manner  some  general  idea  of  its  form  would  be  obtained. 

b.  Galactic  Circle  and  Poles. — The  extensive  survey  made  by 
Sir  William  Herschel  of  the  stars  in  the  northern  hemisphere,  and  con- 
tinued by  his  son,  Sir  John  Herschel,  in  the  southern,  has  proved  that 
there  are  two  points  of  the  celestial  sphere,  diametrically  opposite  to 
each  other,  at  which  the  stars  are  very  thinly  scattered  ;  while  at  and 
near  the  circle  of  which  these  are  the  poles  the  stars  are  so  densely 
crowded  as  to  be  absolutely  countless.  This  circle  lies  very  near  the 
middle  course  of  the  Milky  Way,  and  hence  is  called  the  Galactic 
Circle ;  the  points  at  which  the  stars  are  least  dense  are  called  the 
Galactic  Poles.  It  is  also  found  that  the  decrease  of  the  density  of 
the  visible  stars  in  proceeding  either  way  from  the  plane  of  the 
Galactic  Circle  conforms  to  the  same  law,  but  that  the  density  in  the 
southern  hemisphere  is  at  each  latitude  greater  than  at  the  correspond- 
ing latitude  in  the  northern. 

The  annexed  figure  represents  the  general  form  of  a  section  of  this  Trast 
cluster,  or  stratum  of  stars,  S  being  the  place  of  the  sun ;  S/,  the  position 
of  the  plane  of  the  Galactic  Circle ;  6  5,  the  Galactic  Poles.  It  will  be 

QUESTIONS. — n.  By  whom  was  this  theory  first  suggested  ?  Herschel's  investigations? 
Mode  of  estimating  its  form  ?  b.  What  are  the  Galactic  circle  and  poles  ?  How  found  ? 


THE    STARS.  249 

obvious  that  at  the  visual  lines  S  e  and  S/  the  stars  must  appear  most 
dense,  and  at  S6  least ;  while  at  intermediate  points,  the  density  will  vary 
with  the  obliquity  of  the  visual  lines  ;  and  as  S/  is  nearer  the  northern 
confines  of  the  stratum  than  the  southern,  more  stars  must  be  visible  in 

Fig.  117. 


SECTION   OF   THE   GALACTIC   STRATUM. 

the  southern  hemisphere  than  in  the  northern ;  the  number  of  stars  depend- 
ing in  each  direction  upon  the  length  of  the  visual  line.  The  apparent 
separation  of  the  Milky  Way  is  accounted  for  by  supposing  the  sun  to  be 
placed,  as  indicated,  near  the  point  where  the  two  branches  diverge. 

c.  Dimensions  of  the  Galactic  System. — The  thickness  of  this 
stratum  of  stars  Herscliel  supposed  to  be  about  80  times  the  distance 
of  the  nearest  star  from  the  solar  system ;  but  that  its  extreme  length 
is  equal  to  2,000  times  that  distance.  To  move  from  one  extreme  point 
of  this  vast  space  to  the  other,  light  would  require  about  7,000  years. 

352.  PROPER  MOTION  OF  THE  STARS. — The  stars  do  not 
always  remain  precisely  in  the  same  places  with  respect  to 
each  other,  but  in  long  periods  of  time  perceptibly  change 
their  relative  positions,  some  approaching  each  other,  and 
others  receding.  This  apparent  change  of  position  is  called 
their  proper  motion. 

CL.  The  first  astronomer  to  whom  the  idea  of  a  proper  motion  of  the 
stars  (that  is,  a  motion  of  the  stars  themselves,  independent  of  annual 
parallax)  occurred  was  Ilalley.  Comparing  the  anciently  recorded  places 
of  Sirius,  Arcturus,  and  Aldebaran  with  their  positions  as  observed  by 


QUESTIONS.— c.  Dimensions  of  the  Galactic  System  ?    352.  What  is  the  proper  mo- 
tion of  the  stars?    a.  How  found  ? 


250  THE    STAKS. 

himself  in  1717,  and  making  every  allowance  for  the  variation  in  the 
obliquity  of  the  ecliptic,  he  still  found  differences  of  latitude  amount- 
ing to  37',  42',  and  33',  respectively,  for  which  he  could  not  account, 
except  on  the  supposition  that  the  stars  themselves  had  changed  their 
positions.  This  was  confirmed  by  Cassini  in  1738,  who  ascertained 
that  Arcturus  had  apparently  moved  5'  in  152  years,  while  the  neigh- 
boring star  rj  Bootis  had  been  nearly  if  not  quite  stationary.  The  star 
61  Cygni  has  a  considerable  proper  motion,  having  changed  its  position 
in  fifty  years  nearly  4£'. 

b.  Motion  of  the  Solar  System  in  Space. — In  1783  Herschel 
undertook  the  investigation  of  this  interesting  subject ;  and  finding 
that  in  one  part  of  the  heavens  the  stars  approached  each  other,  while  in 
the  opposite  part  their  relative  distances  seemed  to  increase,  he  arrived 
at  the  conclusion  that  this  apparent  change  in  the  stars  is  caused  by  a 
real  motion  of  the  solar  system  in  space.  For,  evidently,  if  we  are 
in  motion,  the  stars  toward  which  we  are  moving  will  open  out,  while 
those  from  which  we  are  receding  will  appear  to  come  together ;  and 
as  it  was  observed  by  Herschel  that  the  stars  in  the  constellation 
Hercules  are  gradually  becoming  wider  and  wider  apart,  he  inferred 
that  the  motion  of  the  sun  and  its  attendant  planets  is  in  that  direc- 
tion. The  mean  result  of  the  observations  of  Herschel,  and  several 
distinguished  astronomers  who  in  more  recent  times  have  investigated 
the  subject,  is  that  the  point  toward  which  the  solar  system  is  moving 
is  in  260°  20'  of  right  ascension,  and  33°  33'  of  north  declination, 
which  agrees  very  nearly  with  that  reached  by  Herschel  himself.  The 
annual  angular  displacement  of  a  star  situated  at  right  angles  to  the 
direction  of  the  sun's  motion  and  at  the  mean  distance  of  stars  of  the 
first  magnitude,  is  computed  at  about  V' ;  and  therefore  the  velocity 
of  the  motion  is  estimated  at  about  160  millions  of  miles  in  a  year. 

€.  Central  Sun. — The  hypothesis  that  the  solar  system  is  revolving 
around  a  central  sun  was  first  suggested  by  Wright  in  1750.  Madler 
supposed  that  the  central  sun  is  the  star  Alcyone  in  the  Pleiades ;  but 
it  is  not  thought  by  astronomers  that  sufficient  evidence  exists  for  this 
hypothesis.  All  that  can  be  said  to  be  established  is,  that  the  sun  with 
its  great  retinue  of  revolving;  worlds  is  moving  in  space  toward  a  point 
in  the  constellation  Hercules. 

353.  MULTIPLE  STARS  are  those  which  to  the  naked  eye 

QUESTIONS. — It.  What  motion  has  the  solar  system  ?  TTow  indicated?  To  what 
point  is  it  moving  ?  c.  Central  sun  ?  853.  What  are  multiple  stars ?  Double  stars? 


THE    STABS.  251 

appear  single,  but  when  viewed  through  a  telescope  are 
separated  into  two  or  more  stars.  Those  that  consist  of  two 
stars  are  called  double  stars. 

a.  Double  stars  differ  much  in  their  distance  from  each  other ;  in 
some  cases  being  so  near  as  to  be  separated  only  by  the  most  powerful 
telescopes ;  in  others,  they  are  as  much  as  f  from  each  other.     These 
stars  were   carefully  observed  by   Sir  William  Herschel,   and  have 
received  much  attention  from  the  distinguished  astronomers  of  more 
recent  times.     The  list  of  this  class  of  stars  now  contains  upward  of 
six  thousand,  classified  according  to  their  angular  distances  from  each 
other. 

b.  The  members  of  a  double  star  are  generally  quite  unequal  in 
size.     The  pole-star  consists  of  two  stars  of  the  second  and  ninth  mag- 
nitude respectively,  and  about  18"  apart ;  Rigel  has  a  companion  star 
about  10"  from  it,  and  of  the  ninth  magnitude ;  Castor  consists  of 
two  stars  of  the  third  and  Fig.  us. 

fourth  magnitudes  about  5  ' 

apart ;  y  Virginis  (Gamma 

of   the  Virgin)  is  a  very 

remarkable  star  consisting 

of  two  stars  each  of  the 

fourth    magnitude.      (See 

Fig.  118.)    e  Lyrae  (Epsilon 

of  the  Lyre)  is  an  example    L  POLE-8T AR :  2- 1UGEL :  r>'  CA8TOS ; 

of  a  star  consisting  of  two  stars  each  of  which  is  double,  being  thus  a 

double-double  star.     In   1862,   Sirius  was  discovered,   by   Mr.   Alvan 

Clark,  of  New  York,  to  have  a  minute  companion  star  situated  about 

7"  from  it. 

c.  Colored  Stars. — There  is  considerable  diversity  in  the  color  of 
both  the  single  and  double  stars.     Thus  Vega,  Altair,  and  Spica  are 
white  ;  Aldebaran,  Arcturus,  and  Betelgeuse,  ruddy  ;  Capella  and  Pro- 
cyon,   yellow.     Single   stars  of  a  fiery  red  or  deep  orange   are   not 
uncommon ;    but   among  the  conspicuous    stars    there   is  only  one 
instance  (/3  Librae)  of  a  green  star,  and  none  of  a  blue  one.      Many 


QUESTIONS.— a.  Apparent  distance  of  double  stars?  ft.  Comparative  size  and  color  ? 
Size  of  the  members  of  double  stars  ?  Examples?  r.  Difference  in  the  color  of  single 
stars  ?  Of  double  stars  ?  Complementary  colors  ?  Presented  by  how  many  stars  't 


252  THE    STARS. 

double  stars  exhibit  the  beautiful  and  curious  phenomena  of  comple- 
mentary colors,*  the  larger  star  being  usually  of  a  ruddy  or  orange 
hue,  and  the  smaller  one,  green  or  blue.  In  some  cases,  this  is  found 
to  be  the  effect  of  contrast ;  since,  when  a  very  bright  object  of  a  par- 
ticular color  is  viewed  with  another  less  brilliant,  the  latter,  although 
in  reality  white,  appears  to  have  the  complementary  color  of  the  former. 
In  this  way  a  large  and  bright  yellow  object  will  cause  other  objects 
to  seem  violet ;  and  crimson,  produce  the  effect  of  green.  In  many 
cases,  however,  there  seems  to  be  a  real  difference  in  the  color  of  the 
constituents  of  double  stars ;  for  when  one  of  them  is  concealed  by 
introducing  a  slide  in  the  telescope,  the  other  still  retains  its  color. 

Of  596  bright  double  stars  contained  in  Struve's  catalogue,  120  pairs 
are  of  totally  different  hues.  The  number  of  reddish  stars  is  double 
that  of  the  bluish  stars  ;  and  that  of  the  white  stars  2£  times  as  great  as 
that  of  the  red  ones. 

d.  That  some  stars  have  changed  in  color  is  an  established  fact. 
Ptolemy  and  Seneca  expressly  declare  that  Sirius  was  of  a  reddish  hue  ; 
whereas  now  it  is  of  a  brilliant  white.  Stars  described  by  Flamstead 
were  found  by  Herschel  to  have  changed  in  this  respect ;  and  y  Leonis 
and  7  Delphini  have  changed  since  his  time. 

354.  BINARY  STARS  are  double  stars  one  of  which  revolves 
around  the  other,  or  both  revolve  around  their  common  cen- 
tre of  gravity. 

a.  History  of  the  Discovery, — The  discovery  of  this  connection 
between  the  constituents  of  double  stars  was,  perhaps,  the  grandest  of 
Sir  William  Herschel's  achievements.  It  was  announced  by  him  in 
1803,  after  twenty-five  years  of  patient  observation,  which  he  com- 
menced with  the  view  to  discover  the  stellar  parallax  by  noticing 
whether  any  annual  change  in  the  relative  positions  of  double  stars 
existed.  To  his  astonishment,  he  found  from  year  to  year  a  regular 
progressive  movement  of  some  of  these  bodies,  indicating  that  they 
actually  revolve  one  round  the  other  in  regular  orbits,  and  thus  that 


*  Complementary  colors  are  those  which  being  blended  produce  white. 
They  are  red,  yellow,  and  Hue.  The  complementary  color  of  any  one  of 
these  is  a  combination  of  the  other  two.  Thus  orange  is  complementary  of 
blue  ;  and  green,  of  red. 

QUESTIONS. — d.  Change  of  color  in  stars?  854.  What  are  binary  stars?  a.  How 
discovered  ? 


THE    STARS. 


253 


the  law  of  gravitation  extends  to  the  stars.  These  stars  are  called 
Binary*  Stars,  or  Systems,  to  distinguish  them  from  other  double  stars 
which,  although  perhaps  at  immense  distances  from  each  other,  ap- 
pear in  close  proximity,  because,  as  viewed  from  the  earth,  they  are 
very  nearly  in  the  same  visual  line,  and  therefore  are  said  to  be 
optically  double. 

355.  The  observations  of  Herschel  resulted  in  the  dis- 
covery of  about  50  binary  stars;  but  since  his  time  the 
number  has  been,  according  to  Madler,  increased  to  600. 
Most  of  the  double  stars  are  believed  to  be  binary  systems. 

356.  ORBITS  AND  PERIODS  OF  BINARY  STARS. — A  very 
careful  scrutiny  of  these  bodies  and  their  changes  in  posi- 
tion has  shown  that  they  revolve  in  elliptical  orbits  of  con- 
siderable eccentricity  and  in  periods  greatly  varying  in  length. 

The  following  is  a  list  of  the  most  remarkable  of  these  bodies,  with 
their  periods,  and  the  semi-axes  and  eccentricities  of  their  orbits  : 


NAME. 

PERIOD. 

SEMI-AXIS 
MAJO?. 

ECCENTRICITY. 

Yuars. 

C  Herculis, 

36.3                    1.25 

0.44 

rj  Coronae  Borealis. 

43.6 

0.95 

0.28 

Sirius, 

49. 

7.05 

£  Cancri, 

58.9 

1.29 

0.23 

£  Ursae  Majoris, 

63.1 

2.45 

0.39 

"  Centauri, 

753 

30. 

0.96 

«  Leonis, 

84.5 

0.85 

0.64 

70  Ophiuchi, 

92.8 

4.19 

0.44 

7  Coronas  Austral  is, 

100.8 

2.54 

0.60 

f  Bootis, 

117.1 

12.56 

0.59 

(5  Cygni, 

178.7 

1.81 

0.60 

TJ  Cassiopeise, 

181. 

10.33 

0.77 

7  Virginis, 

182.1 

3.58 

0.87 

o  Coronas  Borealis, 

195.1 

2.71 

0.30 

Castor, 

252.6 

8.08 

0.75 

61  Cygni, 

452. 

15.4 

p  Bootis, 

649.7 

3.21 

0.84 

7  Leonis, 

1200. 

From  the  Latin  word  bini,  meaning  two  by  two. 


QUESTIONS.  — 855.  How  many  discovered  ?    356.  Their  orbits  and  periods  ? 


254 


THE    STARS. 


It  will  be  observed  from  the  preceding  table  that  the  eccentricities  of 
these  orbits  are  as  great  as  those  of  the  comets. 

b.  Dimensions  of  Stellar  Orbits. — In  this  table  the  semi-axis  is 
given  as  seen  perpendicularly  from  the  earth ;  but  to  find  the  actual 
dimensions  of   the  orbit,   the  parallax  must  be  ascertained.      The 
problem  is  then  a  simple  one.     Thus,  the  semi-axis  of  a  Centauri  is 
30" ;  but  since  its  parallax  is  0.9187",  1"  must  at  that  distance  sub- 
tend more  than  the  semi-axis  of  the  earth's  orbit  in  the  proportion 
of  .9187  to  1  ;   that  is,  it  must  be  1.088 ;    and  CO"  must   subtend 
1.088  X  30  =  32.64  times  the  semi-axis  of  the  earth's    orbit,  which 
is  equal  to  about  3,000   millions  of  miles.      Now,  the    eccentricity 
is  .96  ;  and  therefore  the  nearest  distance  to  the  central  star  is  only  .04, 
or  120  millions,  while  the  farthest  distance  is  5,880  millions.  In  the  case 
of  61  Cygni,  the  semi-axis  is  15.4",  while  the  parallax  is  0.3638"  ;  hence, 
1"  subtends  at  its  distance  1  -r-.3638  —  2.75  (nearly) ;  therefore  the 
semi-axis  2.75  X  15.4  =  42.35  times  the  semi-axis  of  the  earth's  orbit, 
which  is  equal  to  3,875  millions  of  miles. 

c.  The  following  list  contains  all  the  stars  whose  parallax  has  been 
found : 


NAME. 

PARALLAX 

NAME. 

PAKALLAX 

a  Centauri, 

0.9187 

a  Lyrse, 

0.155 

61  Cygni, 

0.5638 

Sirius, 

0.150 

21258  Lalande, 

0.2709 

i  Ursee  Majoris, 

0.133 

17415  Oeltzen, 

.247 

Arcturus, 

0.127 

1830  Groombridge, 

.226 

Polaris, 

0.067 

70  Ophiuchi, 

.16 

Capella, 

0.046 

d»  Masses  of  the  Stars. — The  joint  mass,  and  in  some  cases  the 
separate  masses,  of  each  pair  of  revolving  stars  can  be  ascertained, 
when  we  know  their  period  and  distance  from  each  other.  Thus,  taking 
Sirius  for  example,  we  find  its  distance  from  its  companion  star  to  be 
47  times  the  earth's  distance  from  the  sun,  while  its  period  is  49  times 
as  great  as  the  earth's.  Hence,  by  the  law  stated  in  Art.  306,  a,  the 


QTTESTIONS.— b.  Size  of  orbits— how  found?  The  calculation?  c.  What  is  the 
nearest  fixed  star?  Parallax  of  Sirius ?  What  distance  does  it  denote?  Capella? 
d.  Masses  of  the  stars— how  calculated  ? 


THE    STARS.  255 

mass  of  the  sun  being  1,  that  of  Sirius  and  its  companion  is  473-f-49* 
=  43.25.  Now,  it  has  been  discovered*  that  Sirius  is  situated  at  a  dis- 
tance from  the  centre  of  gravity  of  both  revolving  stars  equal  to  16£ 
times  the  earth's  distance  from  the  sun  ;  and  therefore  the  companion 
star  is  47  — 16^  =  30  J  that  distance ;  and  as  their  masses  are  in  inverse 
proportion  to  their  distances  from  the  centre  of  gravity,  the  mass  of 
Sirius  is  to  that  of  its  satellite  as  30|  to  16|,  or  as  123  to  65.  Conse- 
quently, the  mass  of  Sirius  is  iff  X  43^  —  28.3  times  the jnass  of  the 
sun ;  and,  if  the  densities  are  the  same,  its  diameter  is  V28.3,  or  a  lit- 
tle more  than  three  times  that  of  the  sun,  and  its  disc  9  times  as  great. 
But  photometric  measurements  have  shown  that  its  light  is  400  times 
as  great  as  that  of  the  sun  would  be  if  the  latter  were  removed  to  the 
distance  of  Sirius ;  so  that  the  materials  of  this  star  must  be  much 
less  dense,  or  its  light  intrinsically  far  more  brilliant,  than  that  of  the 
solar  orb. 

e.  The  Sun  a  Small  Star. — By  certain  photometric  comparisons 
recently  made  by  Messrs.  Clark  and  Bond  between  the  star  Vega 
(a  Lyrae)  and  the  sun,  it  has  been  shown  that  if  the  latter  body  were 
removed  to  133,500  times  its  present  distance,  it  would  send  us  the 
same  quantity  of  light  as  the  star.  But  the  nearest  star  (a  Centauri) 
is  more  than  200,000  times  as  far  from  us  as  the  sun  ;  and  Vega,  about 
six  times  as  far  as  a  Centauri.  Hence  the  sun,  if  removed  to  the  dis- 
tance of  the  nearest  star,  would  shine  only  as  a  star  of  the  second 
magnitude  ;  and  if  removed  to  the  mean  distance  of  stars  of  the  first 
magnitude,  would  appear  as  a  star  of  the  sixth  magnitude,  and  be  just 
visible  to  the  naked  eye.  It  would  seem  therefore  that  the  sun,  mag- 
nificent luminary  as  it  appears  to  us,  is  only  one  of  the  smallest  or 
least  brilliant  of  the  stars. 

357.  PHYSICAL  CONSTITUTION  OF  THE  STABS. — An  analy- 
sis of  the  light  of  the  stars  indicates  that  they  consist  of 
solid  incandescent  matter  surrounded  with  an  atmosphere 
containing  the  vapor  of  some  of  the  elementary  substances 
existing  on  the  earth ;  such  as  mercury,  antimony,  sodium, 
hydrogen,  etc. 

a.  Spectrum   Analysis. — The  band  of  rainbow  colors,  called  the 

*  By  Mr.  Safford,  of  Chicago. 

QUESTIONS. — e.  Is  the  sun  a  large  or  a  small  star  ?  357.  Physical  constitution  of  the 
stars  ?  How  indicated  ?  a.  Spectrum  analysis — what  is  it  ?  How  was  the  method 
discovered  ? 


256  THE    STAKS. 

solar  spectrum,  produced  by  causing  the  sun's  rays  to  pass  through  a 
piece  of  triangular  glass  called  a  prism,  was  noticed  as  early  as  1802, 
by  Wollaston,  to  be  crossed  by  dark  bands  or  lines ;  and  in  1815, 
Fraunhofer,  by  examining  the  spectrum  with  a  telescope,  discovered 
as  many  as  500  of  such  lines,  and  since  then  the  number  perceived  has 
increased  to  thousands.  Now,  it  has  also  been  observed  that,  when 
the  light  of  any  inflamed  vapor  passes  through  a  prism,  its  spectrum 
consists  of  one  or  more  bright-colored  bands,  differing  in  number, 
relative  position,  and  color,  according  to  the  substance  from  which  the 
vapor  proceeds ;  but  that  when  the  light  of  any  incandescent  but  not 
vaporized  substance  is  made  to  pass  through  the  inflamed  vapor,  the 
bright-colored  lines  are  immediately  changed  to  dark  lines,  the  vapors 
absorbing  from  the  light  the  same  kind  of  rays  which  they  themselves 
emit.  Hence  it  is  inferred  that  the  substances  whose  peculiar  lines  are 
found  in  the  solar  spectrum  are  contained  in  a  vaporous  condition  in 
the  solar  atmosphere,  and  as  many  as  fourteen  have  been  already  iden- 
tified. The  stellar  spectra  also  exhibit  similar  dark  lines,  each  star 
having  a  peculiar  series  of  them ;  and  some  are  recognized  as  produced 
by  the  burning  of  substances  found  on  the  earth.  Thus,  some  of  the 
metals  are  found  in  some  of  the  stars,  and  others  in  other  stars ;  and 
this  is  thought  to  account  for  the  different  colors  which  the  stars  pre- 
sent. Sirius  has  been  discovered  to  have  five  of  our  elements ;  and 
Aldebaran,  nine. 

358.  Stars  that  appear  double  when  viewed  through  an 
ordinary  telescope  are  often  separated  by  more  powerful 
instruments,  into  triple,  quadruple,  or  other  multiple  stars. 

Fig.  119. a.  Examples  are  furnished  by 

the  following  stars:  e  Lyrae,  already 
referred  to,  which  consists  of  two 
stars,  each  of  which  is  double ; 
C  Cancri  (Zeta  of  the  Crab),  com- 
posed of  three  stars,  two  large  and 
one  small ;  6  Orionis  (Theta  of 
Orion),  a  very  remarkable  star, 
consisting  of  four  bright  stars, 
two  of  which  have  small  compan- 
0  OBIOMS.  TBAPKZIUM  OF  ORION.  ion  stars,  thus  forming  a  sextuple 

QUESTIONS.— 363.  What  are  triple  stars,  etc.    a.  Examples?    Trapezium  of  Orion? 


THE     STABS.  257 

star.  From  the  configuration  of  the  four  principal  stars  this  is 
sometimes  called  the  trapezium  of  Orion.  (See  Fig.  119.)  As  all  these 
stars  have  the  same  proper  motion,  they  are  believed  to  constitute 
one  system.  It  is  said  that  a  seventh  star  belonging  to  this  system 
has  been  discovered  by  Mr.  Lassell. 

359.  VARIABLE  STARS  are  those  which  exhibit  periodical 
changes  of  brightness.  The  number  of  such  stars  discov- 
ered up  to  the  present  time  (1867)  is  about  120.  They  are 
sometimes  called  Periodic  Stars. 

a.  Examples.— One  of  the  most  remarkable  of  these  stars,  and  the 
first  noticed  (by  Fabricius    in  1596),  is  Mira — the  wonderful — in  the 
Whale  (o  Ceti).     It  appears  about  12  times  in  11  years ;  remains  at  its 
greatest  brightness  about  a  fortnight,  being  equal  to  a  star  of  the  2d 
magnitude ;  decreases  for  about  3  months,  and  then  becomes  invisible, 
remaining  so  5  months,  after  which  it  recovers  its  brillancy ;  the  period 
of  all  its  changes  being  about  331^  days. 

Algol  (13  Persei)  is  another  remarkable  variable  star  of  a  very  short 
period,  it  being  only  2d  20h  49".  It  is  commonly  of  the  2d  magnitude, 
from  which  it  descends  to  the  4th  magnitude  in  about  3£  hours,  and 
so  remains  about  20  minutes,  after  which  in  3£  hours,  it  returns  to  the 
2d  magnitude  and  so  continues  2d  13b ,  when  similar  changes  recur. 
Observation  shows  that  the  period  of  Algol  is  less  than  it  was  in  for- 
mer years.  Its  variability  was  first  noticed  in  1669.  6  Cephei  is 
remarkable  for  the  regularity  of  its  period,  which  is  5d  8h  47111.  Betel- 
geuse,  one  of  the  four  stars  in  the  great  quadrangle  of  Orion,  has  a  period 
of  200  days.  There  is  a  star  in  Cygnus  the  variations  of  which  are 
effected  in  406  days.  Three  of  the  seven  stars  of  the  Great  Dipper  in 
Ursa  Major  are  variable  stars,  their  periods  extending  over  several 
years.  The  double  star  y  Virginis  is  also  variable,  its  two  component 
stars  having  changed  in  brightness,  the  most  brilliant  becoming  infe- 
rior to  the  other,  a  Cassiopese  is  also  variable  as  well  as  double ;  and 
there  are  several  others.  According  to  Mr.  Hind,  the  color  of  most 
variable  stars  is  ruddy. 

b.  Cause  of  Variable  Stars. — Several  hypotheses  have  been  sug- 
gested to  account  for  these  interesting  phenomena.    One  is  that  these 
bodies  rotate  and  thus  present  sides  differing  in  brightness,  or  obscured 

QUESTIONS.— 359.  What  are  variable  stars?  How  many  discovered?  a.  Mira? 
Algol  ?  Other  examples  ?  6.  Cause  of  variable  stars  ? 


258 


THE    STABS. 


by  spots  similar  to  those  which  are  seen  on  the  solar  disc  ;  another,  that 
their  light  is  obscured  by  planets  revolving  around  them  ;  and  a  third, 
that  their  light  is  diminished  by  the  interposition  of  nebulous  masses, 
since  it  has  been  observed  that  during  their  minimum  brightness  they 
are  often  surrounded  by  a  kind  of  cloud  or  mist.  No  one  of  these 
hypotheses  is  entirely  satisfactory,  and  hence  we  may  conclude  that 
the  true  cause  of  the  variability  of  these  stars  is  unknown. 
c.  The  following  is  a  list  of  the  most  interesting  of  these  bodies  : 


NAME. 

PERIOD. 

CHANGES 
OF  MAGN. 

NAME. 

PERIOD 

CHANGES 
OF  MAGN. 

Days. 

From      to 

Days. 

From      to 

ft  Persei, 

2.86 

a*    4 

a  Herculis, 

88^ 

3       4 

<J  Cephei, 

5.36 

4       5 

o  Ceti, 

33U 

2        0 

17  Aquilae, 

7.17 

8*      4^ 

v  Hydrse, 

449£ 

4      10 

ft  Lyrae, 

12.9 

Si      4i 

rj  Argus, 

46yrs 

1        4 

360.  TEMPORARY  STARS  are  those  which  suddenly  make 
their  appearance  in  the  heavens,  sometimes  shining  with 
very  great  brilliancy;  and,  after  a  while,  gradually  fade 
away,  either  entirely  disappearing  or  remaining  as  faint 
telescopic  stars.  The  latter  are  properly  called  New  Stars. 

a.  Ancient  Instances. — The  first  on  record  was  observed  by  Hip- 
parchus,  in  the  second  century  B.C. ;  and  it  was  the  appearance  of  this 
star  that  prompted  him  to  make  a  catalogue  of  the  stars, — the  first 
ever  executed.  This  star  seems  to  have  been,  noticed  also  by  the 
Chinese,  as  its  appearance  is  mentioned  in  their  chronicles  under  the 
date  of  134  B.C.  Brilliant  stars  appeared  in  or  near  Cassiopeia  in  the 
years  945  and  1264  A.D. 

6.  Star  of  1572.— This  was  a  very  remarkable  one,  and  is  described 
by  Tycho  Brahe,  who  observed  it  attentively.  It  appeared  first  as  a 
star  of  the  first  magnitude,  blazing  forth  with  the  lustre  of  Jupiter  or 
Venus,  and  occasioning  the  greatest  astonishment  not  only  to  scien- 
tific men,  but  to  the  common  observers.  For  a  while  it  was  visible 


QUESTIONS. — c.  The  most  remarkable  of  these  stars?     360.  What  are  temporary 
•tars?    New  stars?    a.  Ancient  instances ?    b.  Tycho' s  star? 


THE    STABS.  259 

even  at  noon.  It  lasted  from  November,  1572,  to  March,  1574, — 17 
months.  Its  color  was  successively  white,  yellow,  red,  and  white 
again ;  and  its  position  in  the  heavens  was  the  same  during  the  whole 
time  it  remained  visible.  This  star  is  supposed  to  be  identical  with 
those  which  appeared  in  945  and  1264,  all  three  being  in  fact  apparitions 
of  a  variable  star  of  a  long  period ;  and  some  astronomers  regard  all 
temporary  stars  as  of  this  character. 

c.  Other  Examples. — In  1604  a  very  splendid  star,  remarkable  for 
its  vivid  scintillation,   shone  forth  in  the  constellation  Ophiuchus, 
and  lasted  15  months.     This  star  was  observed  by  Kepler  and  Galileo. 
In  1670  a  star  appeared  in  Cygnus,  which  attained  the  3d  magnitude 
and  was  visible  for  about  two  years,  blazing  out  suddenly  a  short  time 
before  its  final  disappearance.    On  April  28th,  1848,  a  new  star  of  the 
5th  magnitude  was  discovered  in  Ophiuchus,  which  in  a  few  weeks 
rose  to  the  4th  magnitude,  but  subsequently  dwindled  to  the  12th  mag- 
nitude, and  still  remains  as  a  telescopic  star.    Lastly,  a  new  star  was 
seen  in  May,  1866,  in  Corona  Borealis.     It  first  appeared  of  the  2d 
magnitude,  and  of  a  pure  white  color  ;  but  in  a  week  had  changed  to 
the  4th  magnitude,  and  a  month  afterward  diminished  to  the  9th. 
"  It  is  worthy  of  especial  notice,"  says  Sir  John  Herschel,  "  that  all  the 
stars  of  this  kind  on  record,  of  which  the  places  are  distinctly  indi 
cated,  have  occurred  in  or  close  upon  the  borders  of  the  Milky  Way." 

d.  Cause  of  Temporary  Stars. — No  satisfactory  hypothesis  has  as 
yet  been  advanced  to  account  for  these  phenomena.     Some  have  sup- 
posed that  these  stars  are  revolving    in    elliptical  orbits  of  great 
eccentricity  so  that  they  sometimes  approach  very  near  us,  and  then 
recede  to  great  distances ;  but  this  is  rendered  improbable  by  the  sud- 
den changes  in  brilliancy ;  since,  to  pass  from  the  first  to  the  second 
magnitude,  it  is  computed  by  Arago,  would  require  six  years,  if  the 
star  moved  with  the  velocity  of  light ;  whereas,  that  of  1572  underwent 
this  change  in  one  month,  and  that  of  1866  diminished  to  the  extent 
of  five  magnitudes  in  the  same  time.     Another  hypothesis  is,  that 
extensive  conflagrations  take  place  on  the  surface  of  these  bodies, 
which  in  their  progress  give  rise  to  the  observed  changes  in  color  and 
brightness,  and  'at  their  extinction  leave  the  body  in  an  obscure  state. 
The  latter  hypothesis  has  received  some  support  from  the  recent  inves- 
tigations made  by  Huggins,   Miller,   and  others,  by  means  of  the 
spectrum  analysis ;    for  the  light  of  the  star  of  1866  was  shown  by 

QUESTIONS. — c.  Kepler's  star?    Others?    </.  Cause  of  temporary  stars? 


260  THE    STABS. 

these  experiments  to  proceed  from  matter  in  the  state  of  luminous  gas, 
chiefly  hydrogen.  Hence  it  is  supposed  that,  by  some  great  convulsion, 
large  quantities  of  gas  were  evolved  from  the  star,  that  the  hydrogen 
was  burning  in  combination  with  other  elements,  and  that  the  inflamed 
gas  had  heated  to  incandescence  the  solid  matter  of  the  star.  This 
hypothesis  does  not  involve  the  necessity  of  destruction  ;  but,  as 
remarked  by  Humboldt,  only  "  a  transition  into  new  forms,  determined 
by  the  action  of  new  forces.  Some  stars  which  have  become  obscure, 
may  again  suddenly  become  luminous,  by  the  renewal  of  the  same 
conditions  which,  in  the  first  instance,  developed  their  light." 

361.  Numerous  instances  are  on  record  of  stars  formerly 
known  to  exist  which  have  entirely  disappeared  from  the 
heavens.    These  are  called  Lost  or  Missing  Stars. 

a.  Examples. — Several  of  the  stars  in  the  catalogue  of  Ptolemy 
were  not  to  be  found  in  1433,  when  the  catalogue  of  Ulugh  Beigh  was 
made  at  Samarcand  ;  and  it  is  now  known  that  4  stars  in  Hercules 
have  disappeared,  1  in  Cancer,  1  in  Perseus,  1  in  Pisces,  1  in  Hydra,  1 
in  Orion,  and  2  in  Coma  Berenices.     Sir  William  Herschel  recorded  in 
1781  the  star  55  Herculis ;  but  nine  years  afterward  it  was  invisible,  and 
has  never  been  seen  since.    In  1670,  it  was  remarked  by  Montanari,  a 
distinguished  astronomer,  "  There  are  now  wanting  in  the  heavens  two 
stars  of  the  3d  magnitude  in  the  stern  and  yard  of  Argo.     I  and  others 
observed  them  in  1664,  but  in  1668,  not  the  least  glimpse  of  them  was 
to  be  seen." 

b.  Why  Stars  Disappear. — Some  of  the  instances  mentioned  by 
early  astronomers,  of  lost  stars  may  be  the  result  of  erroneous  entries  ; 
but  those  of  later  times  can  not  possibly  be  accounted  for  in  this  way. 
Revolving  in  orbits,  they  may  have  passed  beyond  the  reach  of  the 
most  powerful  telescope ;  or  they  be  obscured  by  the  interposition  of 
great  nebulous  masses,  and  thus  are  only  concealed  for  a  certain  period, 
which  however  may  comprise  hundreds,  or  even  thousands  of  years. 

362.  STAR-CLUSTERS. — These  are  dense  masses  of  stars  so 
crowded  together,  and  so  far  distant,  that  they  present  a 
hazy,  cloud-like  appearance,  similar  to  that  of  the  Milky 
Way. 

QUESTIONS.— 361.  Lost  stars?    a.  Examples?      b.  Why  do  stars  disappear?    862. 
What  are  star- clusters  ? 


THE    STARS. 


261 


a.  Collections  of  stars  visible  as  such  to  the  naked  eye,  although 
considerably  crowded,  are  called  star-groups.  Such  are  the  Pleiades, 
the  Hyades,  and  the  group  which  constitutes  the  constellation  Berenice's 
Hair.  The  first  of  these  is  a  well-known  object  consisting  of  six  stars 
when  viewed  by  the  naked  eye,  but  exhibiting  about  80  to  the  tele- 
scope. Seven  of  these  stars  have  received  special  names,  Alcyone 
being  the  brightest. 

363.  Among  star-clusters,  a  very  small  number  are  suffi- 
ciently bright  to  be  distinguished  by  the  naked  eye ;  but 
generally  they  require  a  telescope  to  render  them  visible. 

a.     Between     the  Pig.  12O. 

bright  stars  in  Cassi- 
opeia and  Perseus, 
there  is  a  visible  clus- 
ter, one  of  the  most 
glorious  objects  in  the 
heavens.  (Fig.  120.) 
The  remarkable  group 
called  Prcesepe,  or  the 
"  Beehive,"  is  another 
example  of  a  cluster 
visible  without  a  tele- 
scope, but  only  as  a 
spot  of  cloud  It  is 
situated  in  Cancer. 

364.  The  PREVAILING  FORM  of  the  telescopic  clusters  is 
circular,  with  a  gradual  condensation  of  the  luminous  points 
toward  the  centre,  indicating  probably  that  the  real  form 
is  that  of  a  globe.      Some  of  the  clusters  when  viewed 
through  powerful  telescopes  assume  a  much  more  irregular 
appearance,   although   their  general  form  still  appears  to 
be  spherical.     Very  irregular  clusters  are  rare. 

a.  Examples. — A  remarkable  cluster  surrounding  the  star  Kappa 


CLTTSTEB   IN  PEBBEUS. 


QtTEBTtONS. — a.  Star- groups?     Examples?     363.    Are  star-clusters  visible  to  the 
naked  eye?    a.  Examples?  364.  Prevailing  form  of  clusters?  a.  Remarkable  clusters? 


262 


THE    STARS. 


of  the  Southern  Cross 
consists  in  part  of  colored 
stars ;  and  another  in  the 
southern  hemisphere  is 
composed  entirely  of  blue 
stars.  The  one  situated 
between  Eta  and  Zeta  in 
the  constellation  Hercu- 
les is  a  peculiarly  mag 
nificent  object  in  our 
northern  heavens  on  fine 
nights,  and  is  visible  to 
the  naked  eye  as  a  very 
small  nebulous  spot  0* 
faint  star.  In  the  tele- 
scope its  general  appear 
ance  is  considerably 
CLUSTEB  IN  HEBCULES. — Sir  J.  Herscfiel.  changed  by  the  addition 

of  several  outlying  branches.  This  splendid  object  is  represented  in 
Fig.  121,  in  which  its  remarkable  condensation  at  the  central  portions 
is  strikingly  exhibited.  Very  many  objects  of  a  similar  character  are 
visible  in  different  parts  of  the  heavens. 

ft.  These  globular  clusters  are  supposed  to  be  held  together  by  their 
motions  and  mutual  attractions.  That  there  must  be  a  real  conden- 
sation is  obvious  from  a  simple  glance  at  such  an  object  as  that  depicted 
in  Fig.  121 ;  since  the  increase  of  brightness  toward  the  centre  is  far 
too  great  to  be  explained  on  the  supposition  that  the  stars  are  equally 
distributed,  but  appear  closer  together  at  the  centre,  because  the  visual 
line  traverses  there  a  much  greater  portion  of  the  mass. 

c.  The  number  of  stars  contained  in  these  clusters  is  very  great. 
According  to  Arago,  many  clusters  contain  at  least  20,000  collected 
in  a  space,  the  apparent  dimensions  of  which  are  scarcely  a  tenth  as 
large  as  the  disc  of  the  moon.  The  clusters  are  not  equally  distrib- 
uted over  the  heavens,  but  are  most  numerous  in  the  Milky  Way  ; 
while  globular  clusters  most  abound  in  that  region  of  the  Galaxy 
contained  between  Lupus  and  Sagittarius  in  the  southern  hemisphere. 

QTTESTIONS.— b.  Cause  of  the  globular  form?  Are  the  stars  equally  distributed  ?  c. 
Number  of  stars  in  a  cluster  ?  Are  the  clusters  equally  distributed  ? 


CHAPTER   XIX. 


NEBULA. 

365.  NEBULA  are  certain  faintly  luminous  appearances  in 
the  heavens,  resembling  specks  of  cloud  or  mist,  some  just 
visible  to  the  naked  eye,  but  the  greater  part  only  to  be 
discerned  with  a  telescope.    They  resemble  in  their  general 
aspect  the  distant  star-clusters,  but  their  physical  structure 
appears  to  be  very  different. 

366.  Their  DISTANCE  from  us  must  be  immense,  since 
they  constantly  maintain  very  nearly  the  same  situation 
with  respect  to  each  other  and  to  the  stars.    Their  magni- 
tudes also  must  be  inconceivably  vast. 

a.  History  of  their  Discovery, — It  is  only  in  quite  recent  years 
that  any  distinction  could  be  positively  made  between  nebulse  *  proper 
and  those  immense  star-clusters  which  present  a  nebulous  appearance 
on  account  of  their  great  distance.  The  first  of  these  objects  mentioned 
in  the  annals  of  astronomy  was  discovered  in  1612,  by  Simon  Marius, 
a  German  astronomer.  This  was  the  nebula  situated  in  the  girdle  of 
Andromeda.  In  1656,  Huyghens  discovered  the  great  nebula  in  Orion, 
which  he  compared  to  an  "  opening  in  the  heavens  through  which  a 
brighter  region  beyond  was  visible."  In  1716,  Halley  could  enumerate 
only  six,  to  which  he  added  a  few  by  his  own  discoveries  ;  and  during 
the  next  half  century,  the  number  was  augmented  to  about  100.  The 
labors  of  Sir  William  Herschel,  directed  to  the  investigation  of  this 
department  of  astronomy  for  more  than  twenty  years,  enabled  him  in 

*  Nebula  is  a  Latin  word  meaning  a  little  cloud.    Plural,  nebulce. 

QUESTIONS.— 365.  What  are  nebul»  ?  866.  Their  distance  from  as  ?  a.  When  and 
by  whom  discovered  ? 


264  NEBULAE. 

1802  to  publish  a  catalogue  of  2,500  nebulae  and  clusters ;  and  the 
subsequent  researches  of  his  son,  Sir  John  Herschel,  in  the  southern 
hemisphere  has  increased  this  number  to  more  than  5,000.  Very  great 
additions,  however,  have  been  made  to  our  knowledge  of  these  inter- 
esting objects  by  the  labors  of  Lord  Rosse,  aided  by  the  largest 
reflecting  telescope  ever  constructed,  and  by  the  application  of  the 
spectrum  analysis. 

367.  Nebulae  are  distinguished  from  clusters  by  not  being 
resolved  into  stars  when  viewed  through  the  most  powerful 
telescopes,  presenting  the  appearance  of  diffuse  luminous 
substances,  filling  vast  regions  of  space,  and  differing  in 
form,  and  degree  of  condensation. 

a.  Resolvable  and  Irresolvable  Nebulae.  —  Herschel  at  first 
thought  all  nebulae  resolvable  into  stars  ;  but  his  subsequent  investi- 
gations convinced  him  that  this  was  an  error  ;  and  he  accordingly 
divided  these  objects  into  resolvable  and  irresolvable  nebula  ;  the  first 
being  those  vast  star-clusters  which  exhibit  a  nebulous,  or  cloudy 
aspect,  because  of  their  comparatively  crowded  condition  and  great 
distance  from  us ;  and  the  second,  according  to  his  conceptions,  im- 
mense aggregations  of  self-luminous  matter,  of  great  tenuity,  but 
gradually  condensing  into  solid  bodies  like  the  sun  and  stars.  This 
bold  conception  of  Herschel's  had  been  entertained  by  Tycho  Brahe 
and  Kepler,  who  suggested  that  the  new  stars  seen  in  their  time  were 
caused  by  aggregations  of  the  ethereal  matter  filling  space.  The 
first  discoverers  of  the  nebulae  also  noticed  an  essential  difference 
between  the  light  of  these  great  phosphorescent  masses  and  that  of 
the  stellar  clusters,  fancifully  comparing  the  former  to  glimpses  of  the 
empyrean  disclosed  by  rents  or  chasms  in  the  celestial  vault.  Laplace 
applied  this  conjecture  of  Herschel's,  under  the  name  of  the  "  Nebular 
Hypothesis  "  to  the  solar  system,  in  order  to  explain  the  manner  of  its 
evolution.  (See  page  202.)  Many  of  the  irresolvable  nebulae  of  Sir 
William  Herschel  having  been  resolved  by  the  great  telescope  of  Lord 
Rosse,  or  having  given  indications  of  being  resolvable  into  stars,  the 
opinion  came  to  be  almost  universally  entertained  that  all  nebula  are 
star-clusters,  some  so  distant  that  light  requires  millions  of  years  to 
pass  from  them  to  us.  But  the  spectrum  analysis  has  proved  this  to 

QTTEBTIONS.— 367.  How  distinguished  from  clusters  ?  a.  How  has  this  distinction 
been  established  ? 


NEBULA.  265 

be  erroneous,  by  showing  that  these  luminous  masses  consist  of 
gaseous,  not  solid  matter  ;  so  that  Herschel's  hypothesis  would  seem  to 
be  established.  These  diffuse  and  attenuated  substances  constitute 
thus  a  peculiar  class  of  objects  in  the  starry  heavens,  and  are  the 
nebulae  defined  in  the  text,  although  some  astronomers  still  continue  to 
classify  them  with  tbe  clusters  which  have  a  nebulous  appearance. 

368.  Nebulae    abound    chiefly  in   those   regions   of   the 
heavens  in  which  the  stars  are  least  numerous,  that  is,  in 
the  vicinity  of  the  Galactic  Poles,  and  are  more  uniformly 
spread   over  the   zone  which   surrounds   the   South   Pole. 
Where  stars  are  excessively  abundant,  nebula?  are  rare. 

a.  Herschel  found  this  rule  to  be  without  exception ;  and  whenever, 
during  a  brief  interval,  no  star  passed  into  the  field  of  his  telescope, 
as  in  the  diurnal  motion  the  heavens  swept  by  it,  he  was  accustomed 
to  say  to  his  secretary,  "  Prepare  to  write  :  nebulae  are  about  to  arrive." 

369.  Nebulae  may  be  divided,  according  to  their  form, 
into  the  following   six  classes;    namely,  elliptic,  annular, 
spiral,  planetary,  stellar,  and  irregular  nebulae. 

370.  ELLIPTIC   NEBULAE  are  such  as  Fis-  122- 
have  the  elliptical  or  oval  form.     They 

are  quite  numerous  and  are  of  various 
degrees  of  eccentricity. 

a.  Examples.  — A  remarkable  nebula  of  this 
kind  is  represented  in  Figure  122.  It  is  situated 
in  the  right  foot  of  Andromeda.  The  most 
noted  of  these  nebulas  is  that  in  the  girdle 
of  Andromeda,  already  referred  to  as  the  first 
nebula  discovered.  It  is  one  of  the  grandest 
and  least  resolvable  in  the  heavens,  and  is 
visible  to  the  naked  eye ;  so  much  so,  indeed, 
that  it  is  strange  none  of  the  ancient  astrono- 
mers ever  observed  it.  In  very  powerful  tele- 
scopes, such  as  that  at  Cambridge,  Mass.,  it 
presents  some  quite  striking  peculiarities  of 

QUESTIONS.— 368.  Where  are  nebulae  abundant?  a.  Herschel1  s  remark  ?  369.  How 
are  nebulae  classified  ?  370.  Elliptic  nebulae  ?  a.  The  nebula  in  Andromeda. 


266 

form,  two  dark  clefts  appearing  to  divide  it  longitudinally  ;  while  ha 
length,  as  viewed  through  this  instrument  by  Prof.  Bond,  is  4°,  and 
its  breadth,  2£°. 

Fig.  123. 


ANNULAR  NEBULA  IN  LYBA. — 1.  Sir  John  Herschel  ;  2.  Lord  Rosse. 

371.  ANNULAR  NEBULAE  are  such  as  have  the  form  of  a 
ring.    These  are  very  rare,  the  heavens  affording  only  four 
examples. 

a.  The  most  remarkable  one  is  found  in  Lyra,  situated  between 
the  stars  Beta  and  Gamma,  and  may  be  seen  with  a  telescope  of  mod- 
erate power.  It  is  slightly  elliptical  and  has  the  appearance  of  a  flat 
oval  ring,  the  opening  occupying  somewhat  more  than  one-half  of  the 
diameter.  The  central  portion  is  not  altogether  dark,  but  is  crossed 
with  faint  nebulous  streaks,  compared  by  some  to  gauze  stretched  over 
a  hoop.  The  telescope  of  Lord  Rosse  shows  fringes  of  stars  at  its 
inner  and  outer  edges.  (See  Fig.  123.)  The  other  annular  nebulae  are 
two  in  Scorpio,  and  one  in  Cygnus. 

372.  SPIRAL  NEBULAE  are  such  as  have  the  form  of  one 
or   more   spirals   or  coils ;  in   some   cases  presenting  the 
appearance  of  continuous  convolutions,  or  whorls ;  in  oth- 
ers, of  great  spiral  arms  or  branches  projecting  from  a  central 
nucleus. 

a.  The  discovery  of  nebulse  of  this  remarkable  form  is  due  to  Lord 
Rosse,  no  indication  of  it  whatever  having  been  afforded  by  the  great 

QUESTIONS. — 371.  What  are  annular  nebulne  ?  Their  number?  «.  The  most  remarka- 
ble ?  3T2.  What  are  spiral  nebulae  ?  a.  By  whom  discovered  ?  The  most  remarkable  ? 
Describe  the  one  in  Leo. 


NEBULA.  267 

telescope  of  Sir  William  Herschel.  The  grandest  object  of  this  kind 
is  found  in  Canes  Venatici.  Brilliant  spirals,  unequal  in  size  and 
brightness,  and  apparently  overspread  with  a  multitude  of  stars, 
diverge  from  the  central  nucleus,  the  whole  suggesting  the  idea  of  a 
rotary  movement  of  considerable  rapidity,  and  the  play  of  forces  at 
which  the  imagination  is  startled  when  it  contemplates  the  immensity 
of  space  filled  by  this  wondrous  object. 
Fig.  124. 


SPIKAL  NEUUL^S  IN  iEO.-^Lord  Itosse. 

Figure  124  represents  a  very  beautiful  object  of  this  kind  in  the  lower 
jaw  of  Leo,  the  spiral  form  being  clearly  brought  out  in  Lord  Rosse's  great 
telescope.  The  convolutions  are  nearly  all  closed,  so  as  to  assume  almost 
the  form  of  concentric  ellipses,  the  central  one  containing  what  appear  like 
several  distinct  stellar  nuclei. 

373.  PLANETARY  NEBULAE  are  those  which,  in  their  cir- 
cular or  slightly  elliptical  form,  their  pale  and  uniform  light, 
and  their  definite  outline,  resemble  the  larger  and  more  dis- 
tant planets  of  our  system. 

a.  One  of  the  most  striking  of  this  class  is  found  in  Ursa  Major 
(near  /?),  the  light  of  which,  in  Sir  John  Herschel's  drawing,  is  quite 
uniform  ;  but  when  seen  through  Lord  Rosse's  telescope,  it  presents 
the  appearance  depicted  in  Fig.  125  (No.  1).  The  disc  is  about  3'  in 
diameter,  and  exhibits  a  double  luminous  circle  with  two  dark  openings, 


QUESTIONS.— 37S.  What  are  planetary  nebulre  ?    a.  What  examples  are  given,  and 
how  described  ? 


268  NEBULA. 

each  containing  a  bright  but  partially  nebulous  star.  No.  2  in  the 
same  figure,  represents  a  nebula  near  «  (Kappa)  in  Andromeda,  which, 
though  perfectly  round  in  Herschel's  drawing,  appears  in  Lord  Rosse'a 
like  a  luminous  ring  surrounded  by  a  wide  nebulous  border. 

Fig.   125. 


PLANETABY    NKBUL.fi.       1,  IN    UKSA.   MAJOB  ,    2,  IN    ANDROMEDA. 

b.  The  number  of  planetary  nebulae  discovered  is  about  25,  three 
fourths  of  which  are  in  the  southern  hemisphere.  Several  described  by 
Sir  John  Herschel  are  of  a  blue  color,  in  some  cases  with  a  tinge  of 
green. 

c.  The  size  of  these  objects  must  be  amazingly  great.     That  of 
LTrsa  Major,  if  no  farther  from  us  than  the  nearest  star,  a  Centauri, 
would  be  sufficiently  large  to  fill  a  space  equal  to  three  times  the  orbit 
of  Neptune  ;  but  there  is  reason  to  believe  that  it  is  more  than  1,000 
times  as  large  as  this.     How  vast  then  must  be  the  size  of  such  a  neb- 
ula as  that  in  Andromeda ! 

In  Fig.  126,  1  and  2  are  representations  of  planetary  nebulae.  The 
former  is  in  Aquarius  and  is  quite  remarkable  for  its  brightness. 

374.  STELLAK  NEBULA  are  those  which  appear  to  envelope 
one  or  more  brilliant  spots  or  points,  resembling  stars  sur- 
rounded by  a  nebulous  border  or  ring.  There  are  several 
varieties,  the  most  important  of  which  are  nebulous  stars. 


QUESTIONS.— ft.  Their  number  ?    c.  Size  ?    374.  What  are  stellar  nebulse  ? 


NEBULJE.  260 

375.  NEBULOUS  STARS  are  stars  encircled  by  a  nebulous 
border,  which  in  some  cases  has  a  clearly  defined  outline,  in 
others  gradually  shading  off  into  the  general  appearance  of 
the  sky. 

Fig.  126. 


a.  Such  stars  differ  from  other  stars  only  in  having  this  apparently 
nebulous  atmosphere.  If  the  nebula  is  circular  the  star  occupies  the 
centre  of  it ;  while  in  the  case  of  some  that  are  elliptical,  two  stars  are 
placed  at  the  foci. 

In  the  above  cut  (Fig.  126),  No.  5  represents  a  remarkable  nebulous  star 
in  Cygnus.  The  star  is  of  the  llth  magnitude,  and  is  at  the  centre  of  a 
perfectly  circular  nebula  of  uniform  light,  and  about  15'  in  diameter.  No.  4  is 
a  stellar  nebula  in  Sobieski's  Shield,  of  an  elliptic  form,  and  having  two  stars 
at  the  foci  of  the  ellipse.  These  stars  are  described  by  Sir  John  Herschel 
as  of  a  gray  color.  No.  3  is  the  representation  of  a  nebula  bearing  a  re- 
semblance to  a  comet.  It  is  found  in  the  tail  of  Scorpio.  There  are  several 
other  instances  of  such  nebula?,  which  from  their  appearance  are  called 
conical  or  cometary  nebulae.  In  the  case  of  each  the  stellar,  or  bright,  point 
is  at  one  extremity  of  the  nebulous  mass. 

b.  It  has  been  thought  by  some  that  the  connection  between  these 
nebulae  and  stars  is  not  real,  but  is  merely  the  effect  of  perspective,  the 
one  being  situated  behind  the  other,  but  separated  by  a  wide  interval. 
It  is,  however,  very  improbable  that  so  many  of  these  nebulae  should 
be  found  with  stars  placed  exactly  at  their  centres,  some  gradually  be- 
coming fainter  towards  their  borders,  if  there  were  no  physical  con* 
nection  between   them  ;  especially  as,  up  to   the  present  time,  no 
difference  in  their  proper  motion  has  been  discovered. 

c.  It  seems,  therefore,  probable  that  these  are  stars  encompassed 
with  very  extensive  atmospheres  in  the  same  way,  perhaps,  as  the 
luminous  centre  of  our  system  is  enveloped  in  what  we  call  the  Zodical 

QUESTIONS. -375.  Nebulous  stars?  c.  How  different  from  other  stars?  What  ex- 
amples represented  in  Fig.  126  ?  fe.  Is  the  connection  between  the  star  and  nebula  op- 
tical or  physical  ?  c.  Their  probable  nature  ? 


NEBULA. 

Light,  the  sun  itself  being  in  reality  a  nebulous  star ;  but  the  atmos- 
pheric envelopes  of  the  other  stars  referred  to  must  be  vastly  more 
extensive.  The  one  in  Cygnus,  described  above  as  15'  in  diameter,  and 
therefore  extending  450"  beyond  the  central  star,  must,  if  the  object 
is  only  as  far  from  us  as  a  Centauri,  have  an  extent  equal  to  fifteen 
times  the  distance  of  Neptune  from  the  sun. 

376.  IRREGULAR  NEBULA  are  such  as  have  no  symmetry 
of  form  and  scarcely  any  distinctness  of  outline,  and  are  also 
remarkable  for  the  diversity  of  brightness  which  they  exhibit 
at  different  parts. 

a.  Arago  remarks  of  these  diffuse  masses  ol  nebulous  matter,  that 
"  they  present  all  the  fantastic  figures  which  characterize  clouds  car- 
ried away  and  tossed  about  by  violent  and  often  contrary  winds."  The 
most  remarkable  of  these  objects  are  the  following: 

Fig.  127. 


CRAB   NEBULA   IN   TAURUS. — Lord  RoKSe. 


QUESTIONS.— 8T6.  What  are  irregular  nebulae  ?    a.  Their  general  appearance  ? 


NEBULA. 

1.  The  Crab  Nebula  in  Taurus  (Fig.  127).— This  singular  object  has 
an  elliptic  outline  in  ordinary  telescopes,  but  in  Lord  Rosse's  great 
reflector  it  presents  an  appearance  which  has  been  fancifully  likened 
to  a  crab  or  lobster  with  long  claws. 

2.  The  Great  Nebula  in  Orion. — This  is  probably  the  most  magnifi- 
cent of  all  the  nebulae.     It   is  very  irregular  in  form ;  of  immense 
extent,   covering  a  surface  more  than  40'  square  ;   and  consists  of 
patches  varying  considerably  in  brightness.     Near  the  famous  sextuple 
star  0  Orionis,  already  described,  it  is  very  brilliant ;  but  other  portions 
are  quite  dim,  and  some  absolutely  black.     It  was  thought  that  por- 
tions of  this  nebula  had  been  resolved  into  stars  by  the  telescopes  of 
Lord  Rosse  and  Prof.  Bond  ;  but  the  experiments  of  Messrs.  Huggins 
and  Miller  with  the  spectroscope  have  proved  conclusively  the  gaseous 
nature  of  this  object;  the  light  from  the  brightest  part  of  the  nebula 
giving  a  spectrum  of  only  three  bright  lines,  indicating  the  presence 
of  hydrogen,  nitrogen,  and  a  third  substance  unknown.     The  examina- 
tion of  other  portions  gave  similar  results. 

8.  The  Great  Nebula  in  Argo. — This  is  another  very  irregular  and 
extensive  nebula,  covering  a  space  equal  to  five  times  the  disc  of  the 
moon.  It  contains  a  singular  vacancy  of  an  irregular  oval  form  near 
the  centre,  and  not  very  far  from  the  variable  star  Eta  "  It  is  not 
easy,"  says  Sir  J.  Herschel,  "  to  convey  a  full  impression  of  the  beauty 
and  sublimity  of  the  spectacle  which  this  nebula  offers  as  it  enters 
the  field  of  the  telescope,  ushered  in  as  it  is  by  so  glorious  a  pro- 
cession of  stars,  to  which  it  forms 
a  sort  of  climax  "  This  nebula  is 
remarkably  destitute  of  any  indica- 
tions of  resolvability. 

4  The  Dumbbell  Nebula  (Fig. 
128.)— This  object  is  found  in  Vul- 
pecula,  and  derives  its  name  from 
its  singular  appearance  as  viewed 
through  a  telescope  of  moderate 
power.  In  Lord  Rosse's  telescope 
it  assumes  a  form  of  less  regu- 
larity, and  appears  to  consist  of  in-  DCMB-BKLL  NEBULA.— Herschel. 


QUESTIONS.— How  is  the  Crab  Nebula  described  ?    The  Great  Nebula  in  Orion  ?    That 
in  Argo  ?    Dumb-bell  nebula  1 


272  NEBULA 

numerable  stars  mixed  with  a  mass  of  nebulous  matter.     These  may 
be  only  centres  of  condensation. 

5.  The  Magellanic  Clouds. — These  are  situated  in  the  southern  hem- 
isphere and  not  far  from  the  pole,  and  are  called  sometimes  Nubecula 
Major  and  Minor,  or  the  Greater  and  Lesser  Cloudlets.  The  former  is 
in  Dorado  ;  the  latter  in  Toucan.  These  objects  are  distinguished  for 
their  great  extent,  the  larger  one  covering  a  space  of  about  42  square 
degrees,  and  the  smaller  being  of  about  one-fourth  that  extent,  but  of 
greater  brightness.  The  telescope  of  Sir  J.  Herschel  decomposed  them 
into  separate  stars,  star-clusters,  and  numerous  distinct  nebulae.  In 
the  larger  cloud.  Herschel  counted  582  single  stars,  46  star-clusters,  and 
291  nebulae  ,  and  in  the  smaller  cloud,  200  single  stars,  7  star-clusters, 
and  37  nebulae.  In  the  immensity  of  their  extent  and  the  diversity 
of  objects  which  they  present,  they  are  cnly  ccmparalie  to  that  ap- 
parently greatest  of  all  clusters,  the  Milky  Way. 

377.  DOUBLE  NEBULA  are  those  which  indicate  by  their 
close  proximity  to  each  other  that  they  have  a  physical 
connection.  More  than  50  of  such  objects  have  been 
enumerated,  the  component  nebula?  of  which  are  not  more 
than  5'  apart. 

Fig.  129  represents  an  object  of  this  kind,  found  in  Gemini.    It  is  com- 
posed of  two  rounded  masses, 

129' terminated  by  brilliant  ap- 
pendages and  enveloped  in  a 
nebulous  mass,  the  whole  sur- 
rounded by  light  luminous 
arcs  resembling  fragments  of  a 
nebulous  ring. 

378.  VARIABLE  KEB- 
UL^:  are  those  which  un- 
dergo changes  in  appar- 
ent form  and  brightness. 
a.    Several    instances    of 

.-Lord  jfem.  such     changes     have     been 

positively     ascertained     by 
Struve,  D' Arrest,  Hind,  and  other  distinguished  astronomers.      The 

QUESTIONS.— Magellanic  Clouds?    37T.  What  are  double  nebulae?    378.   What  are 
variable  nebulse  ?    a.  Instances? 


NEBULAE.  273 

great  nebulae  in  Orion  and  Argo  have  exhibited  undoubted  varia- 
tions of  a  marked  character.  When  Sir  J.  Herschel  observed  the  latter 
in  1838,  the  star  Eta  was  of  the  1st  magnitude  and  situated  in  the 
densest  part  of  the  nebula ,  but  in  1867,  an  observer  at  Hobart-town, 
found  it  within  the  central  vacuity,  and  only  of  the  6th  magnitude. 
It  is  also  stated  that  the  vacuity  is  materially  different  in  form  from 
that  represented  by  Herschel.  Another  observer  at  Madras  confirms 
these  statements,  and  adds  that  the  nebula  has  varied  considerably  in 
brightness  while  under  his  own  observation. 

Some  of  the  smaller  nebulae  exhibit  changes  similar  to  those  of  the 
variable  stars.  In  1861,  it  was  noticed  by  D' Arrest  that  one  in  Tau- 
rus had  disappeared ;  and  circumstances  indicated  that  this  event  had 
occurred  in  1858.  In  December,  1861,  the  nebula  reappeared,  increased 
in  brightness  for  several  months,  but  in  December,  1863,  could  not  be 
found.  Phenomena  of  a  similar  character  were  observed  by  Sir  W. 
Herschel.  Two  stars,  surrounded  by  circular  nebulae  in  1774,  presented 
no  traces  of  these  envelopes  in  1811.  If  these  objects,  as  it  was  formerly 
supposed,  were  all  composed  of  distinct  stars,  it  would  be  scarcely  pos- 
sible to  conceive  how  such  variations  or  disappearances  could  occur, 
particularly  within  the  short  periods  mentioned ;  but  on  the  hypothe- 
sis that  they  consist  of  diffuse  luminous  matter,  each  nebula  being  a 
separate  mass,  these  changes  harmonize  with  what  we  see  among  the 
stars  themselves. 

379.  STRUCTURE  OF  THE  UNIVERSE. — The  universe  has 
heen  supposed,  by  many  modern  astronomers,  to  consist  of 
an  infinite  number  of  star-clusters  similar  to  the  galaxy,  and 
situated  at  inconceivably  immense  distances  from  it  and 
from  each  other.  In  view,  however,  of  the  recent  discov- 
eries as  to  the  nature  of  the  nebulae  proper,  this  hypothesis 
can  not  be  considered  as  established ;  and  the  true  structure 
of  the  universe  remains  a  problem  to  be  solved. 

a.  The  hypothesis  alluded  to  was  a  deduction  from  that  which,  sup- 
posing every  nebula  to  be  resolvable  into  stars,  banished  those  that 
seemed  irresolvable  to  the  uttermost  depths  of  space.  Spectrum  an- 
alysis having  exploded  this  idea,  we  are  necessarily  compelled  to 
discard  those  extravagant  conceptions  as  to  the  distance  of  these  visible 

QUESTIONS. — 379  Prevailing  theory  as  to  the  structure  of  the  universe?  a.  How 
aff?cted  by  recent  discoveries?  What  is  proved  by  them? 


274  NEBULA. 

objects.  For,  since  we  can  not  penetrate  to  the  remotest  parts  of  the 
galaxy,  or  resolve  every  portion  of  its  milky  light  into  stars,  there  is  no 
reason  for  believing  that  those  star-clusters,  which  are  readily  resolv- 
able, are  beyond  the  confines  of  our  sidereal  system ;  while  the  fact> 
already  mentioned,  that  clusters  and  nebulae  are  invariably  abundant 
where  stars  are  rare,  and  as  invariably  wanting  where  stars  abound, 
affords  presumptive  evidence  that  all  these  bodies  are  physically  con 
nected  with  the  same  great  system  of  the  universe  of  which  the  galaxy 
itself  is  a  portion. 

b.  What  other  creations  occupy  the  infinitude  of  space  beyond  the 
reach  of  human  vision  aided  by  the  utmost  efforts  of  optical  and  me- 
chanical skill,  we  can  neither  know  nor  perhaps  conceive.  There  is 
reason  for  believing  that  light  itself  is  gradually  absorbed  and  thus 
extinguished  in  its  journey  ings  from  those  remote  regions  of  the  uni- 
verse, long  before  it  could  reach  our  little  orb  and  give  us  intelligence 
of  the  worlds  from  which  it  spedi  But  that  the  works  of  God  are 
infinite  in  extent  as  they  are  in  perfection  and  beneficent  design,  we 
can  not  but  believe ;  nor  as  we  contemplate  the  wonders  and  glories 
of  the  starry  heavens — those  unfathomable  abysses  lit  up  by  millions 
of  suns,  can  we  refrain  from  bowing  in  adoration  and  gratitude  to 
Him  who  has  endowed  us  with  the  intellectual  power  (far  more  won- 
drous than  even  these  worlds  themselves)  to  discover  and  survey 
their  vastness  and  magnificence,  and  with  those  moral  and  spiritual 
capacities,  by  the  due  cultivation  of  which  we  may  prepare  ourselves 
for  an  existence  in  that  future  world  where  we  shall  be  enabled,  in  a 
far  higher  degree,  to  contemplate  His  power  and  to  understand  His 
infinite  wisdom  and  beneficence. 

QTJTSTIONB. — ft.  Other  creations  in  thp  infinitude  of  space  ?  Why  not  discoverable? 
Feelings  excited  by  a  contemplation  of  the  starry  heavdns  ? 


APPENDIX. 


Cl       02       %        g        H 

»    >    a    P   5 

sips 

?>     .      *     :      : 


to     oc     o    I  s>sn- 


as.     o 
^      o 


Mean  Diam- 
eter. 


3- 


Oblateness. 


.—       —        »• 
os      to      p 

Sr    °°    a 


p  Of  OS  M- 
OS  OO  CO  rf^. 
<f  rfi-  Of  tO 


to      (->• 

s*  ^   SP, 

OS         rf*.         tO 


fe 


tO         M-         M.  CO 


OS        CO         M-        Of 
«H         O        O        H^ 


CO        CO        CO 


OS        -3        Of        tO 


ol 


Mass,  © 
being  1. 


Density  com- 
pared with 
water. 


Mean  Dis- 
tance in 
Millions. 


Eccentricity 
of  Orbit. 


Inclination 
of  Orbit. 


Sidereal 
Period. 


Ul 


Synodic 
Period. 


333 


£     o«     oo 

3     P     ? 


Time  of  Ro- 
tation. 


o 


Inclination 
of  Axis. 


276 


APPENDIX. 


TABLE  II.  — ELEMENTS  OF  THE  MINOR  PLANETS. 


NAME. 

Number. 

Mean  Dis- 
tance. 

_>» 

i§ 

a 

Inclination 
of  Orbit. 

Sidereal 
Period. 

Discoverer. 

2 

C3 

p 

FLORA. 

8 
43 
71 

40 
18 
80 
12 
27 
4 
30 
52 
84 
7 
9 
62 
63 
25 
20 
67 
44 
6 
83 
21 
42 
19 
79 
11 
17 
46 
89 
29 
13 
5 
14 
32 
91 
47 
70 
54 
78 
23 
37 
15 
51 
66 
85 
26 
73 
3 
75 
77 

e'a=i 

2.2014 
2.2034 
2.2661 
2.2677 
2.2956 
2.2963 
2.3344 
2.3467 
2.3733 
2.8655 
2.3657 
2.3675 
2  386'^ 
2.3866 
2.893 
2.395 
2.4008 
2.4097 
2.4217 
2.422 
2.4259 
2.4287 
24354 
2.44 
2.4411 
2.4431 
2.4519 
2.4735 
2.5265 
2.5498 
2.554 
2.5766 
2.5771 
2.586 
2.5873 
2.5958 
2.5959 
2.6133 
2.6197 
2.6228 
2.6271 
2.6414 
2.6437 
2.6491 
2.6512 
2.6536 
2.6561 
2.6666 
2.6684 
2.6698 
2.6719 

.157 
.168 
.12 
.046 
.217 
.2 
.219 
.173 
.09 
.126 
.066 
.238 
.231 
.123 
.185 
.126 
.254 
.144 
.185 
.151 
.203 
.084 
.162 
.225 
.158 
.195 
.099 
.128 
.164 
.18 
.074 
.087 
.187 
.166 
.083 

.287 

.183 
.204 
.205 
.232 
.177 
.187 
.287 
.158 
.191 
.(i87 
.043 
.257 
.307 
.136 

0        / 

5    58 
8    28 
5    24 
4    16 
10      9 
8    87 
8    23 
1    35 
7      8 
2      6 
9    57 
9    22 
5    28 
5    36 
3    34 
5    47 
21    35 
41 
5    59 
8    42 
14    47 
5      2 
8      5 
8    34 
1    33 
4    87 
4    37 
5    36 
2    18 
16    11 
6      8 
16    31 
5    19 
9      8 
5    29 

s""i 

11    38 
5      7 
8    38 
10    13 
3      7 
11    44 
2    48 
8      4 
11    53 
3    36 
2    25 
13      1 
5      0 
2    28 

Yrs.  dys. 
3      97 
8      99 
3    150 
8    151 
8    174 
3    175 
3    207 
3    217 
3    229 
3    223 
8    223 
8    225 
3    240 
8    251 
8    256 
3    258 
3    263 
8    270 
8    280 
3    281 
3    284 
8    287 
3    292 
3    296 
3    297 
8    299 
3    806 
3    325 
4        6 
4      26 
4      30 
4      50 
4      51 
4      58 
4      59 

i"  '67 

4      82 
4      88 
4      90 
4      94 
4    107 
4    109 
4     114 
4    116 
4    118 
4     120 
4     129 
4    131 
4    133 
4    134 

Hind 

1847 
1857 
1861 
1856 
1852 
1864 
1850 
1858 
1807 
1854 
1858 
1865 
1847 
1848 
I860 
1861 
1853 
1852 
1861 
1857 
1847 
1865 
1852 
1856 
1852 
1863 
1850 
1852 
1857 
1866 
1854 
1850 
1845 
1851 
1854 
1S66 
1857 
1S61 
1858 
1863 
1S52 
1855 
1851 
1857 
1861 
1865 
1853 
18(i2 
1S04 
1862 

ARIADNE  
FERONIA  . 

Poison 

C.  H.  F.  Peters. 
Goldschmidt... 
Hind  

HAKMONIA  

MKLPOMENE  
SAPPHO  
VICTORIA  

Pogson  

Hind 

EUTERPE  

Hind 

VESTA  
URANIA 

Olbers  

Hind 

NEMAUSA.  .  .  . 

Laurent  
Lnther  
Hind 

CLIO  

IRIS  

METIS 

ECHO  

Ferguson  
De  Gusparis  
Chitcornac  
De  Gasparis  
Poison 

AUSONIA 

PHOCEA  

M  A6SILIA 

ASIA  

NYSA  

Goldschmidt... 
Hencke  . 

HKHE.  .  .  .  . 

BEATRIX  

De  Gasparis  
Goldschmidt... 
Pogson  
Hind  

LUTETIA. 

Isis  

FORTUNA  

KURYNOME          .       . 

Watson  
De  Gasparis  
Luther  

PAKTHENOPE  
THETIS  

HESTIA. 

Stephan  
Marth  

AMPHITRITE  
EGERIA  
ASTR.EA  
IRENK  
POMONA  

De  Gasparis  
Hencke  
Hind  .. 

Goldschmidt.  . 
Stephan  
Goldschmidt.  .  . 

Luther  

MELKTK  
PANOPEA  

CALYPSO  

DIANA 

Hind  
Luther  
De  Gasparis  
Ferguson  
H.  P.  Tuttle  .  .  . 
Peters 

THALIA  

FlUKS 

KUNOMIA  

VIRGINIA  

MAIA 

lo.  

PROSERPINE  

Luther  
Tuttle  

JlTNO.                  ...    . 

Harding  
Peters  .   

EuRvnicK   

FRIGGA  

APPENDIX 


277 


ELEMENTS  OF  THE  MINOR  PLANETS  —  CONTINUED. 


NAME. 

Number. 

ji 

Eccentricity. 

Id 
c  £ 
1? 

Sidereal 
Period. 

Discoverer. 

I 

ANGELINA  

64 

e's=i. 

2.681.9 

.128 

o      / 
1     20 

T       dys. 
142 

Tempel  

1S61 

CIRCE  

84 

2.6863 

in 

5    26 

147 

Chacornac  .  .    . 

1855 

CONCOBDIA 

58 

2.7008 

.042 

5      2 

160 

Luther  

18CO 

ALKXANORA  
OLYMPIA  
EUGENIA 

55 
60 
<\*> 

2.7123 
2.7181 

2.7212 

.197 
.117 

08 

11    47 

8    87 
6    85 

171 
172 
179 

Goldtchumlt..  . 
Ihucornnc  
Goldschiuidt 

36t8 
IfCO 

1K7 

LEDA  

88 

2.7401 

.155 

6    58 

196 

Chacorn:;c  .... 

16tG 

ATAI.ANTA  
NIOBE  

86 

79 

2.7461 

2.7564 

.301 
.174 

18    42 
23    19 

201 
219 

Goldschmidt..  . 
Luther  

1K5 
1861 

PANDORA..  . 

56 

2.7591 

.145 

7    14 

218 

Searle  

1858 

ALCMENE 

82 

2.7608 

226 

2    51 

214 

Luther 

1£64 

CURES  

1 

2.7667 

.08 

10    86 

4    2iO 

Piazzi  .... 

1801 

L^ETITIA 

39 

27671 

.115 

10    '22 

4    221 

1856 

DAPHNE  

41 

2.7691 

.266 

15    ,'9 

4    223 

Goldschiuidt  .  . 

PALLAS. 

2 

2.7696 

24 

84    43 

4    228 

Olbers      ... 

1S02 

TlIISBE 

88 

2  7702 

165 

5    15 

4    224 

Peters 

U66 

GALATEA  
BKLLONA 

74 

28 

2.7777 
2  7785 

.238 
15 

8    59 
9    21 

4    231 
4    232 

Tempel  

IS  62 
1854 

LET(  

69 

2  7804 

188 

7    57 

4    288 

1861 

TERPIBCHORE  
POLYHYMNIA  
AGLAIA  

81 
S3 

48 

2.8568 
2.8641 

2.8812 

.212 

.839 
.182 

7    £5 
1    16 
ft      (» 

4    802 
4    8C9 
4    825 

Tempel  
Chticornac  
Luther  

18C4 
18.*4 
1857 

CALLIOPE. 

22 

2  9107 

.088 

13    44 

4    853 

Hind  

1852 

PSYCHE  

"Ifi 

2.9287 

.185 

3      4 

5 

DeGasparis.... 

HFSPERIA 

68 

2  9717 

.174 

8    28 

5      45 

Schinparelli.... 

1861 

DANAE  

LKUCOTHE  A  

f9 

85 

2.S84S 
8.0(  66 

.162 
.217 

18    15 
8    12 

5      57 

5      78 

Goldschinidt... 
Luther  

1^60 
1855 

PALES 

ro 

S.fiSkS 

.287 

3      9 

5    150 

Goldschuiidt... 

1857 

SEMELE  

8fi 

8(108 

.2(5 

4    48 

5    158 

Tietjen  

1866 

KUROPA 

fW 

3.(  999 

.101 

7    25 

5    K8 

Goldschiuidt... 

1858 

DORIS  

4ft 

.8.11  94 

.077 

6    29 

5    176 

ki 

HM 

ANTIOPE 

% 

8  1188 

.148 

2    16 

5    Ib6 

Luther  

1866 

61 

812H7 

.169 

2    12 

5    196 

Fiirster  ..  . 

IS  60 

TIIFMIS 

94 

81431 

.117 

49 

5    209 

DeGaspuris.... 

1853 

HYGEIA  

10 

3.1511 

.1 

8    49 

5    217 

1849 

EUPHROSYNB  

81 
57 

3.1527 
8  l.*65 

.22 

104 

26    27 

15      8 

5    218 
5    222 

Ferguson  
Luther 

1854- 
1859 

FREIA     ... 

76 

83877 

.188 

2      2 

6      86 

D'Arrtst  

1862 

65 

84205 

.12 

8    28 

6    119 

Tempel  

1861 

SYLVIA  

87 

8.4927 

6    193 

Pogson  

18C6 

MINERVA 

<WI 

"Watson  

1807 

UNDINA  

98 

Peters  

AURORA 

94 

Watson  

" 

95 

Luther  

u 

^EGINA      .      ... 

96 

Borelly  

1838 

97 

Tempel  

u 

98 

Peters  

M 

J^~  MELETE  was  at  first  supposed  by  Goldschmidt  to  be  Daphne,  but  was  recog- 
nized to  be  a  new  planet  on  the  calculation  of  its  elements  by  Schubert  in  1858.  Hence 
its  number  is  sometimes  given  as  66. 


278 


APPENDIX. 


ELEMENTS  OF  THE  MINOR  PLANETS  —  CONTINUED, 


NAME. 

Number. 

Mean  Dis- 
tance. 

Eccentricity. 

Inclination 
of  Orbit. 

Sidereal 
Period. 

Discoverer. 

v 

& 

<w 

Tempel 

100 

Watson  .  .  . 

HELENA  

101 

« 

102 

Peters  

103 
104 

Watson  

u 

105 

II 

106 

u 

- 

INDEX. 


A  BERBATrON    of  light,  245. 

Aerolites,  225. 

Algol,  257. 

Alignments,  method  of,  242. 

Altitude,  57. 

true  and  apparent,  59. 
Altitude  of  the  pole,  59. 
Anali'.mma,  use  of,  71. 
Angle,  11. 

measurement  of  12. 

of  vision,  11. 
Annual  equation  of  the  moon,  180. 

parallax,  229. 
Annular  eclipse,  139. 

nebula;,  260. 
Anomalistic  year, 
Apogee,  112. 
Apparent  motions  of  the  heavenly  bodies,  18 

of  the  inferior  planets,  165. 

of  the  sun,  63. 

of  the  superior  planets,  168. 
Argo,  great  nebula  in,  271. 
Aspects  of  the  planets,  43. 
Asteroids  (see  Minor  Planets). 
Astrsea,  discovery  of,  200. 
Atmosphere  of  Jupiter,  178. 

of  Mars,  173. 

of  the  moon,  125. 

of  Saturn,  185. 

of  the  sun,  107. 
August  meteors,  224. 
Axial  inclinations  of  the  planets,  41. 

rotations  of  the  planets,  40. 

velocity  of  Jupiter,  175. 
Azimuth,  57. 

DAILY'S  Beads,  40. 

Beer  &  Miidler's  charts,  125,  173. 

Belts,  Jupiter's,  177. 

Saturn's,  185. 
Biela's  comet,  211,  220. 
Binary  Stars,  252. 
Bode' a  law,  39,  196. 
Brorseu's  comet,  211. 

CARDINAL  points,  how  determined,  23. 

of  ecliptic,  67. 
Celestial  equator,  64. 

latitude  and  longitude,  70. 
Central  sun,  250. 


Centre  of  gravity  of  solar  system,  207. 
Centriftural  force,  29,  30,  88. 

law  of,  175. 
Centripetal  force,  29. 
Ceres,  discovery  of,  199. 
Chaldeans,  17,  140,  141. 
Chinese  observations,  17,  130,  258. 
Circles,  great  and  small,  15. 

of  daily  motion,  57. 
Civil  day,  95. 
Clusters  of  stars,  260. 
Coal-sack,  247. 
Colored  stars,  251. 
Colures,  67. 
Comet,  Biela's,  220. 

Donatrs,  222. 

Encke's,  218. 

Halley's,  216. 

of  1680,  216. 

of  1744,  212,  220. 

of  1811,221. 

of  1843,  221. 

of  1844,  212. 

of  1861,  222. 

of  1862,  222. 
Comets,  209. 

direction  of  motion,  212. 

elements  of,  211. 

elliptic  or  periodic,  211. 

nucleus  of,  215. 

number  of,  213. 

orbits  of,  209. 

size  of,  213. 

tails  of,  214. 
Comparative  axial  inclinations,  41. 

densities,  26. 

distances.  38. 

eccentricities,  34. 

magnitudes,  i5. 

masses,  £7. 

orbital  velc  cities,  40. 

times  of  rotation,  42. 
Conic  sections,  210. 
Conjunction,  43. 
Constant  day  and  night,  74. 

at  Jupiter,  176. 

at  Mare,  172. 
Constellations,  231. 
catalogue  of,  233. 
classification  of,  232. 


INDEX. 


Constellations,  history  of,  234. 

number  of,  232. 

table  for  learning,  239. 
Copernican  system,  18. 
Copernicus,  a  lunar  mountain,  12T. 
Corona,  in  solar  eclipse,  140. 
Cotidal  lines,  14T. 
Craters,  lunar,  127. 
Crystalline  spheres,  20. 
Culmination,  56. 
Cusps,  of  Mercury,  153. 

of  Venus,  153. 

D'ABBEST'S  comet,  211. 
Day  and  night,  73. 
Declination,  67. 

circle  of,  67- 
Degree,  length  of,  89. 
Densities  of  the  planets,  26. 
Derivative  tides,  147. 
De  Vico's  comet,  211. 
Difference  of  time,  51. 

of  longitude,  51. 
Digits,  138. 

Dip  of  the  horizon,  55. 
Distances  of  the  planets,  37. 
Diurnal  arc,  59. 
Donati's  comet,  220. 
Double  stars,  251. 

EABTH,  density  of,  102. 

diameter  of,  90. 

distance  from  the  sun,  99. 

general  form  of,  49. 

rotation  of,  17. 

size  of,  to  find,  88. 

spheroidal  form,  88. 
Earth's  orbit,  eccentricity  of,  101. 

variation  in,  86. 
Earthshine  on  the  moon,  123> 
Eccentricity,  14. 

of  planets'  orbits,  34 

of  stellar  orbite,  253. 
Eclipse,  first  recorded*  141. 
Eclipses,  131. 

annular,  139. 

central,  138. 

cycle  of,  139. 

number  in  a  year,  135. 

phenomena  of,  140. 

total  and  partial,  138. 
Ecliptic,  64. 

obliquity  variable,  92k 
Ecliptic  limits,  132,  133. 
Elements  of  a  planet's  orbit,  205» 

of  a  comet's,  211. 
Ellipse,  defined,  14. 

major  and  minor  axes  of,  14. 
Elliptic  comets,  211. 

nebulae,  265. 
Elongation,  44. 

extreme,  150. 

of  planets  at  Neptune*  192. 
Encke's  comet,  218. 
Epicycle,  31. 


Equation  of  the  centre,  35. 

of  time,  95. 
Equator,  50. 
Equinoctial,  64. 

spring  tides,  146. 
Equinoxes,  64,  66. 
Establishment  of  the  port,  147. 
Evection,  129. 
Evening  and  morning  star,  47, 163. 

FACULJS,  105. 

Faye's  comet,  211. 

Fire  balls,  225. 

Fixed  stars,  18.    (See  Stars.) 

Fizeau's  experiments  on  light,  182. 

Foci,  14 

Force,  centrifugal,  29,  30. 

centripetal,  29. 

impulsive  and  continuous,  29. 

GALACTIC  circle  and  poles,  248. 
Galaxy,  246. 
Galileo,  18,  104. 
Galle,  Dr.,  finds  Neptune,  186. 
Geocentric  place,  205. 
Georgium  Sidus,  192. 
Gravitation,  law  of,  29. 
how  discovered,  30. 

Great  inequality  of  Jupiter  and  Saturn,  206. 
Greek  alphabet,  232. 

HALLEY'S  comet,  216,  217. 
Harvest  moon,  117. 
Heliocentric  place,  205. 
Herschel,  Sir  W.,  183,  185,  190,  248,  250, 
253,  264. 

theory  of  solar  spots,  107. 

nebular  theory,  264. 

Herschel,  Sir  J.,  34,  109,  153, 174,  177,  271. 
Horizon,  54. 

dip  of,  55. 

rational,  55. 

Horizontal  parallax,  60. 
Horrox,  163. 
Hour  angle,  67. 

circle,  67. 

Hourly  motions  of  the  planets,  40. 
Humboldt,  110,223. 
Hunter's  moon,  118. 
Hyperbola,  210. 

INCLINATION  of  orbit,  36,  37. 

of  axis,  41. 
Inequalities,  204. 

Inequality  of  Jupiter  and  Saturn,  206, 
Inertia,  146. 
Inferior  planets,  149. 

~JUNO,  discovery  of,  199. 
Jupiler,  174. 
Jupiter's  satellites,  178. 

eclipses  of,  18<>. 

libration  of,  181. 

KEPLEB'S  laws,  30,  33. 


INDEX 


281 


Kepler's  3d  law,  applied,  158, 163. 
Kepler's  star,  269. 

LAPLACE,  130, 148,  181,  206. 
Lassell,  23,  186,  188,  197,  251. 
Latitude  and  longitude,  49. 
Law,  Bode's  39,  196. 

of  oblateness,  175. 
Laws,  Kepler's,  30,  33. 
Lexell's  comet,  220. 
Librations  of  the  moon,  121. 
Light  and  heat  at  Jupiter,  177, 

Mercury,  154. 

Neptune,  197 

Saturn,  184. 
Light,  aberration  of,  245. 

extinction  of,  in  space,  274. 

intensity  of,  at  different  planets,  109. 

solar,  comparative  intensity  of,  lOtf. 

Telocity  of,  182. 
Limits,  ecliptic,  132, 133. 

transit,  155. 

Longest  day  and  night,  76. 
Longitude,  49. 

how  found,  182. 
Lost  or  missing  stars,  260. 
Lunar  axis,  position  of,  122. 

inclination  of,  122. 
Lunar  day  and  night,  123. 
Lunar  mountains,  126. 

height  of,  l.:7. 

eclipses,  135. 
Lunar  irregularities,  128. 

theory,  130. 
Lunation,  116. 

M ABLER' s  chart  of  Mars,  173, 

of  the  moon,  125, 
Magellanic  clouds,  272. 
Major  and  minor  axes,  14. 
Mars,  168. 

distance  found  by  phases,  169. 
parallax  of,  how  found,  171. 
ruddy  color  of,  174, 
polar  hemispheres  of,  178. 
Mass,  25. 

of  earth  and  sun,  102. 
of  the  planets,  27. 

of  sun  and  planets,  how  to  find,  207. 
of  Sirius,  254. 
Mean  and  true  place,  35. 
Mercury,  149. 

mass  of,  151,  219. 
mountains  in,  153. 
transits  of,  155. 
Meridian  of  a  place,  56. 
Meridian  circles,  50. 

length  of  a  degree  of,  89. 
Meridian  altitude  of  the  sun,  66. 
Meteoric  dust,  227. 
epochs,  224 
rings  or  streams,  224. 
satellites  of  the  earth,  226. 
transits,  227. 
theory  of  sun's  heat,  111. 


Meteoric  theory  of  minor  planets,  228. 
Meteors,  223. 

August,  224. 

cosmical  origin  of,  225. 

November,  227. 

number  of,  2'25. 

physical  origin  of,  2'?8. 
Milky  Way,  246.     (Sec  Galaxy.) 
Million,  idea  of,  S8. 
Minor  planets,  199. 

magnitude  of,  26,  201. 


origin  of,  202. 

principal  discoverers  of,  200. 
Mira,  the  wonderful  star,  26J. 
Moon,  112. 

harvest,  llf. 

hbrations  of,  121, 

phases  of,  114. 

synodic  and  sidereal  periods  of,  116. 
kloonlight,  in  winter,  118. 

in  polar  regions,  118. 
horning  and  evening  star,  217. 
Motion,  laws  of,  28. 

curvilinear,  29. 

resultant,  29. 
Mutual  attractions  of  the  planets,  202. 

tf  ADIB,  56. 

Nasmyth's  "  Willow  Leaves,"  107. 
Nebular  hypothesis,  202. 

theory  of  Herschel,  264. 
Nebula  in  Andromeda,  265. 

in  Argo,  271. 

in  Lyra,  266. 

in  Orion,  271. 

(Jr.  b,  zTl. 

Dumb-bell,  271, 
Nebulse,  263. 

annular,  266. 

cometary,  269. 

double,  272. 

elliptic,  265. 

irregular,  270. 

planetary,  267. 

resolvable  and  irresolvable,  26* 

spiral,  266. 

stellar,  268. 

variable,  iT2. 

gaseous  nature  of,  264. 

where  abundant,  265. 
Nebulous  stars,  269. 
Neptune,  194 

discovery  of,  195. 

satellite  of,  197 

supposed  ring,  197. 
Newton,  30,  34,  144. 
Nocturnal  arc,  59. 
Nodes,  36,. 

November  meteors,  227. 
Nutation,  244 

how  discovered,  245. 
solar  and  lunar,  245. 
OBLATENESS,  of  the  earth,  90. 
law  of,  175 


INDEX. 


Oblique  sphere,  53. 
Obliquity  of  the  ecliptic,  66. 

variation  in,  92. 
Occultation,  141. 
Olbers,  199,  200 

theory  as  to  asteroids,  202. 
Opposition,  43. 
Orbits,  planetary,  28-3T. 

eccentricity  of,  34. 

inclination  of,  ilG. 

of  comets,  20,  210. 

of  meteors,  22T. 

of  satellites,  180,  190. 

of  stars,  253,  254. 

PALI.  AS,  199. 

Parabola,  210 

Parallactic  inequality,  lunar,  130 

Parallax,  59. 

of  the  moon,  60,  112. 

of  the  sun,  164,  171. 

of  the  stars,  229,  254. 
Parallel  sphere,  53. 
Parallels  of  latitude,  51. 
Pendulum,  a  measure  of  gravity,  88. 
Penumbra,  131. 
Perigee,  112. 
Periodic  comets,  211. 

meteors,  223. 

stars,  253. 

times  of  the  planets,  39. 
Perpetual  apparition,  circle  of,  58. 

ocoultation,  circle  of,  59. 
Perturbations,  204. 
Phases  of  Mars,  168. 

of  the  moo  i,  114. 

of  Venus,  156. 

Phenomena  of  the  heavenly  bodies,  17. 
Photosphere  of  the  sun,  107. 
Plane,  defined,  10. 
Planetary  nebulae,  267. 
Planets,  20. 

comparative  densities,  26. 

elements  of  orbits,  205, 

major  and  terrestrial,  25. 

masses  of,  27. 

mutual  attractions  of,  204. 

orbital  eccentricities,  34. 

orbital  inclinations,  37. 

orbital  velocities,  40. 

relative  distances,  38. 

rotations,  41. 
Pleiades,  243. 
Polar  circles,  76. 
Polaris  (see  Pole-star), 
Poles,  of  a  circle,  15. 

galactic,  248. 

terrestrial,  50. 
P.)le-star,  244. 
Positions  of  the  sphere,  58. 
Praesepe,  261. 
Precession  of  the  equinoxes,  70. 

cause  of,  fiO. 

effect  of,  91,  24 1. 

lunar,  122. 


Prime  meridian,  50. 

vertical,  57. 

Priming  and  lagging  of  the  tides,  14T. 
Primitive  tides,  147. 
Problem  of  Three  Bodies,  204. 
Problems  for  the  globe,  52,  70,  79,  06,  24L 
Ptolemaic  system,  18. 
Ptolemy,  18,  129,  238. 
Pythagoras,  18. 

QUADBATUBE,  144. 

Quartile,  45. 

Questions  for  exercise,  48. 

RADIATING  streaks  on  the  lunar  disc,  127. 
Radius- vector,  32. 
Refraction,  61. 

amount  at  different  altitudes,  63 

effect  of,  62. 

effect  in  a  lunar  eclipse,  141. 
Resisting  medium,  217. 
Resolvable  nebulas.  264. 
Retrogradation,  arc  of,  169. 

duration  of,  169. 
Retrograde  motion.  163. 
Right  ascension,  67. 

sphere,  58. 

Ring  mountains,  lunar,  12T. 
Rings,  meteoric,  224. 

of  Saturn,  185. 
Roemer,  182. 
Rotation  of  nebulae  266. 

planets,  42. 

Saturn's  rings,  187. 

satellites.  190. 

stars,  257. 

sun,  42. 

SATELLITE  of  Neptune,  197. 

of  Sirins,  251,  255. 
Satellites  of  Jupiter,  178. 

Saturn,  183. 

Uranus,  23,  194. 
Saturn,  182. 

belts  of,  185. 

celestial  phenomena  at,  190. 

density,  184. 

equatorial  velocity  of,  184. 

mass,  184. 

oblateness,  183. 

rings,  1S5-189. 

satellites,  189,  190, 

telescopic  view  of,  187. 
Schroeter,  153,  159. 

Sehwabe's  researches  on  solar  spots,  106. 
Secondary  circles,  50. 

planets  (see  Satellites). 
Secular  acceleration,  lunar,  130. 

perturbations,  204. 

variations,  205. 


length  of,  unequal,  84. 
variable,  86. 
Selenograpy,  124 
Sextile,  45. 


INDEX. 


283 


Shadow,  earth's,  181. 

moon's  1ST. 

Shooting  stars  (see  Afeteora). 
Sidereal  day,  92. 
month,  11(5. 
year,  96. 

period  of  Jupiter,  175. 
Mars,  172. 
Mercury,  154. 
moon,  116. 
Neptune,  196. 
Saturn,  183. 
Uranus,  193. 
Venus,  162. 

Signs  of  the  ecliptic,  68. 
of  planets  (see  each). 
Sine  of  an  angle,  101. 
Snow  and  ice  at  Mars,  173. 
Solar  day,  93. 
eclipses,  135. 
heat,  theory  of,  111. 
light,  intensity  of,  109. 
parallax,  163,  171. 
spots,  103-108. 
system,  18. 

motion  of,  250. 
Solstices,  64. 
Spectrum  analysis,  255. 
Sphere,  defined,  14. 
positions  of,  58. 

Spheroid,  oblate  and  prolate,  16. 
Stability  of  Saturn's  rings,  1ST. 
solar  system,  207. 


apparent  places  of,  244. 

binary,  252. 

colored,  251. 

double,  251. 

distance  of,  230. 

list  of  principal,  240. 

lost  or  missing,  260. 

magnitudes  of,  230. 

multiple,  250,  256 

names  of,  232,  240. 

nebulous,  269. 

new,  258. 

parallax  of,  229. 

physical  constitution  of,  255. 

proper  motion  of,  249. 

scintillation  of,  229. 

shooting  or  falling,  223. 

temporary,  260. 

variable,  257. 
Star  clusters,  260. 

conflagration  of  a,  259. 

figures,  241 

groups,  261. 

Kepler's,  253. 

names,  240. 

showers,  228. 

TychoX  258. 

Stationary  points,  167-169 
Structure  of  the  universe,  273. 
Sun,  100. 

a  small  star,  255. 


Sun,  a  nebulous  star,  270. 

apparent  and  real  diameters  of,  101. 

apparent  motions  of,  68,  64 

apparent  magnitude,  209. 

distance  from  the  earth,  99. 

inclination  of  axis,  104. 

mass,  102,  207. 

meridian  altitude,  66. 

motion  of,  in  space,  109,  250. 

photosphere  of,  107. 

physical  constitution  of,  107. 

surface  and  volume,  102. 
Sun's  heat  and  light,  111. 
Superficial  gravity  at  Jupiter,  176. 

Mercury,  153. 

Saturn,  184. 

Venus,  159. 
Superior  planets,  168. 
Synodic  period,  45. 
Syzygies,  1 15. 

TELESCOPE,  invention  of,  20. 
Telescopic  views  of  Jupiter,  178. 

of  the  moon,  125. 

of  Saturn,  187. 
Temporary  stars,  260. 
Thales,  140. 
Theory,  meteoric.  Ill,  229. 

of  nebulae,  264. 

of  solar  spots,  107. 

of  zodiacal  light,  111. 
Theta  ( Hionis,  256. 
Three  Bodies,  problem  of,  204. 
Tidal  force  of  sun  and  moon,  143. 
Tides,  cause  of,  142. 

equinoctial  spring,  144. 

flood  and  ebb,  142. 

height  of,  145, 148. 

highest,  148. 

how  retarded,  146. 

of  rivers  and  lakes,  148. 

priming  and  lagging,  147. 

primitive  and  derivative,  147. 

why  they  rise  later,  146. 
Tide  waves,  146. 

velocity  of,  148. 
Time,  92. 

equation  of,  95. 
Transits,  meteoric,  227. 

of  Jupiter's  satellites,  180. 

of  Mercury,  155. 

of  Titan,  190. 

of  Venus,  163. 
Trapezium  of  Orion,  256. 
Triangle,  defined,  13. 
Trine,  45. 
Tropics,  74. 
Twilight,  77. 

Twinkling  of  the  stars,  229. 
Tycho  Brahe,  258,  264. 
Tycho,  a  lunar  mountain,  127. 

UMBBA,  131. 
Uranus,  191. 

elongation  of  planets  at,  192. 


284 


INDEX. 


Uranus,  existence  predicted  by  Clairaut, 

218. 

satelites  of,  23,  194. 
sunrise  and  sunset  at,  192. 

VARIABLE  nebulae,  272. 

stars,  257. 
Variation,  lunar,  120. 

of  obliquity  of  ecliptic,  92. 

in  length  of  seasons,  86. 
Velocity  of  solar  system,  110,  250. 
Velocities  of  planets,  40. 
Venus,  156. 

atmosphere  of,  160. 

mountains  in,  159. 

when  most  brilliant,  158 
Vertical  circles,  56. 

sun,  74. 
Vesta,  119. 
Visual  angle,  11. 
Volumes  of  sun  and  planets,  24. 
Vulcan,  22, 149. 


WILSON'S  theory  of  sun's  spots,  107. 
Winnecke's  comet,  211. 
Wolfs  researches  on  sun's  spots,  106. 
Wollaston's  estimate  of  sun's  light,  109. 
discovery  of  lines  in  solar  spectrum, 

256. 
Wright's  theory  of  the  Universe,  5:48. 

YEAB,  anomalistic,  97. 
civil,  96. 

equinoctial  or  solar,  96. 
sidereal,  96. 
tropical,  96. 

ZENITH,  56. 
Zenith  distance,  57. 
Zodiac,  68. 

constellations  of,  233. 
Zodiacal  light,  1 10. 

cause  of.  111. 

theory  of  Chaplain  Jones,  110. 

theory  of  Prof.  Norton,  111. 
Zones,  87. 


ROBINSON'S 

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